To answer this, it will be helpful to break this question down.

Is someone acting out their homosexual desires sinful? Yes.

You shall not lie with a male as with a woman; it is an abomination. Leviticus 18:22 (ESV)

The source of homosexual passion is God allowing people to rebel against him. It is sourced in the rejection of God in a person’s life.

For this reason God gave them up to dishonorable passions. For their women exchanged natural relations for those that are contrary to nature; and the men likewise gave up natural relations with women and were consumed with passion for one another, men committing shameless acts with men and receiving in themselves the due penalty for their error. Romans 1:26–27 (ESV)

Can a Christian have homosexual desires? Yes.

I have counseled homosexuals who have come to Christ. The Holy Spirit and God’s Word have convicted them of the sinfulness in their homosexual actions. While they understand homosexual desire is not the sexual desire God intends for them to have, they still struggle with same sex attraction. In repentance, they have chosen to not act out their homosexual desires but to live celibate lives and avoid situations that tempt them to sin. This is no different from a heterosexual who has strong sexual passions toward the opposite sex choosing to honor God by living in celibacy until marriage. Heterosexual marriage is the only place God gives for us to express and fulfill our sexual desires. Homosexual marriage is not an option (see Genesis 2:18-25)

Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality, 1 Corinthians 6:9 (ESV)

It should be noted that 1 Corinthians 6:9 doesn’t talk about those who have strong heterosexual attraction, but those who express it outside of marriage (sexual immorality and adultery). In the same way, it is not talking about those who have homosexual attraction but those who act it out (who practice homosexuality).

If sexual sin is something you struggle with, thank God for Jesus Christ who washes us clean from our sinful sexual choices.

...And such were some of you. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God. 1 Corinthians 6:11 (ESV)