Can you be a gay Christian?
If, by "gay Christian" you mean someone who is attracted to the same sex, but understands all homosexual acts (regardless if you are in a long-term, committed, and monogamous relationship) falls under the category of sexual immorality, and therefore does not give in to their fleshly desires toward the same sex, then yes you can be a "gay Christian." Like all followers of Christ, this Christian denies their fleshly desires and offers their body as a living sacrifice, holy and pleasing to God.
If, however, by "gay Christian" you mean someone who is still a practicing homosexual (someone who still engages in homosexual acts, and might have a gay partner) but still loves to pray and worship God, then no this person is not a follower of Christ. It's a stretch to call anyone a Christian who refuses to submit their lives (their whole lives) to Christ, carry their own cross and follow His Word. Furthermore, many of these "Christians" find their identity in their sexuality rather than in Jesus Christ, and the god they worship is a god they have made in their image (who views sexuality the way they do). This is someone who doesn't have a sexuality problem; they have a submission problem.
"If you want to be my disciple, you must hate everyone else by comparison--your father and mother, wife and children, brothers and sisters--yes, even your own life. Otherwise, you cannot be my disciple. And if you do not carry your own cross and follow me, you cannot be my disciple."--Luke 14:26-27
Matt Moore, a brother in Christ who struggles with same-sex attraction, provides a great response to this question here.
Dr. Ravi Zacharias offers great insight to this question in this video below: