Yes, in the sense that matters most: it's a matter of personal context and conscience. Nothing in Scripture says that describing your attractions with the word gay is sinful, though in some settings it may be unwise or unhelpful. Faithful Christians who hold a traditional view of marriage land in different places on this, and you can be one of them without being less of a Christian.
That's the short answer. The rest of this post explains where it comes from, because the question is bigger than one word. It's really a question about what "identity" means, and that turns out to be less settled than most assume. This post draws on Pastoral Paper 20 from The Center for Faith, Sexuality & Gender, "Can Faithful Christians Identify as Gay?", which is free to download at centerforfaith.com/resources. We agree with its conclusion, and we recommend reading it in full.
Why this question gets so heated
The question here is not whether same-sex marriage is a faithful option, and it is not whether experiencing same-sex attraction is itself a sin. This post comes from the position that marriage is between a man and a woman and that attraction is not a sin. The question is narrower: for a Christian who holds those two convictions, is it acceptable to say "I'm gay"?
Christians answer in roughly three ways. Some say it's a matter of personal context and conscience: the word may be unwise in some settings, but there's nothing wrong with it in itself. Some say it's never the best or wisest choice, and that people should be gently guided toward other language. And some say that using the word is itself sinful, that it must be repented of, and in the strongest versions that those who use it may not be genuine Christians. With stakes that high, it's no surprise that people feel strongly. If the third view is right, getting this wrong harms the church's holiness. If the first view is right, getting it wrong harms the church's unity, and it harms real people who are told they have to stop describing their own experience.
What "identity" means, and where it came from
Much of the argument depends on one word, so it helps to know its history. In English, "identity" originally just meant sameness. People did not "identify as" anything. The modern sense, a label for who you are, took hold in the social sciences in the middle of the twentieth century and spread into everyday speech from there. By the 1970s, writers were already complaining that the word was being used for everything, which made it mean very little.
The phrase "identity in Christ" has a similar history. It sounds like it comes straight out of the Bible, but it became popular only in the late twentieth century. What Scripture does say, over and over, is that believers are "in Christ," united to him. That is the deepest truth about any Christian, and nothing here competes with it.
This matters for our question because it removes a false choice. Neither "identity in Christ" nor "identifying as gay" appears in the Bible as a category. So we can't simply set one against the other and declare a winner. Being united to Christ is the foundation of who we are. It does not erase every other true thing about us. We are also sons and daughters, spouses and friends, workers, citizens, and people with particular histories and attractions. Our identities are layered, and a person can honestly name one layer without claiming it is the bottom one.
The same word covers very different things. "Identity" can name something objective, like age or height. It can name a relationship, like father or friend. It can name a job, a belief, a group, or a personality type. Even a single phrase means different things to different people. Someone who says "I'm a Republican" might mean it organizes their whole life, and someone else might mean only that they're registered to vote that way.
What the word gay can mean
At its most basic, gay means attracted to the same sex. That is how most dictionaries define it, and it's how most people use it. But like any identity word, it can carry more than that, depending on who is speaking. Someone who says "I'm gay" might also mean that they are in, or hope for, a same-sex relationship. They might mean that they're committed to celibacy. They might mean they're unsure how they'll respond to their attractions, or that they dislike them, or that they feel neutral about them. They might mean they belong to a community, or that they hold certain political views, or that they don't fit the stereotypes at all.
Context tells you which of these is meant. If someone asks "are you gay, straight, bisexual, or asexual?", an answer of "I'm gay" is exactly what the question calls for. Without context, it's easy to assume the wrong thing, and that is where most of the trouble starts.
How much weight the word carries
The word also carries different weight for different people. At one end, someone might use it to mean only that they're attracted to the same sex, while their faith, family, work, and other commitments matter far more to them. In the middle, someone's orientation may shape how they see themselves in society and remind them that they're different from most of the people around them, without being the most important thing about them. At the other end, someone's orientation may drive many of their choices, from friendships to politics to where they spend their time, and come up in nearly every conversation.
These aren't three boxes. They sit on a spectrum, and the same word can land anywhere on it. Two Christians can both say "I'm gay" and mean very different things. That is why the word alone tells you very little about what someone believes or how they live.
What this means for you
If you're a gay Christian trying to decide how to describe yourself, you aren't required to use the word, and you aren't forbidden from using it. Some people find it honest, because it's the plain English word for their experience and avoiding it can start to feel like dodging the truth. Some find it helpful for sharing their faith with people who assume that no gay person could follow Jesus. Some find that saying it takes away shame they have carried for years. Others find that a different phrase serves them better, or that the word has become a distraction, or that they needed one word in one season of life and a different one later. All of that falls within what the Bible leaves to conscience and wisdom.
A few questions are worth asking yourself. What do you mean when you say it? What do the people in front of you hear when you say it? Does it help you be honest with God and with others, or does it pull your attention toward your sexuality more than you want? Are you using it because it is accurate, or to make a point you could make some other way? There's no formula. The answers can change with the setting and with the stage of life you're in.
Whatever you choose, the word is not what matters most. What matters is how you are following Jesus. A person's words are a poor guide to their faithfulness, and their life is a better one.
Where soulintension stands
On this site, we generally use the word gay in its ordinary sense, because it is the most widely understood word for the experience. That is a choice about audience and context, not a rule. Many Christians prefer "same-sex attracted" because it fits their experience better, or their church, or the person they are talking to, and we are glad to use that phrase when it is the better fit. Neither word is the one correct answer. A person may sensibly use one with a coworker, another with a pastor, and a third with a close friend, and may change their mind over time.
We hold a traditional view of marriage and we hold that orientation is not a sin, and we think the choice of language belongs to the individual's conscience. We won't argue with anyone about which word they use. The next two posts in this series look at the reasons Christians give for using the word gay and the objections others raise, and then at how pastors, parents, and friends can respond well.