Absolutely yes! That is the whole point!
Jesus came to seek and to save that which was lost (Luke 19:10).
1 Timothy 2:3-4
This is good, and pleases God our Saviour, 4who wants all people to be saved and to come to a knowledge of the truth.
2 Peter 3:9
The Lord is not slow in keeping His promise, as some understand slowness. He is patient with you, not wanting anyone to perish but everyone to come to repentance.
The scriptures specifically talk about homosexuals who had become Christians. The 1 Corinthians 6 passage lists practising homosexuals amongst those who will not enter the Kingdom of God, but then says…
1 Corinthians 6:11
And that is what some of you were. 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.
There is nothing in scripture that suggests that homosexuality is unforgivable. On the contrary, practising homosexuals were saved in the early church, not because their lifestyles were acceptable to God but by God’s grace (note all the passive verbs), in the name of the Lord Jesus Christ and by the power of the Holy Spirit.
Because homosexual acts are sinful (like innumerable other sexual and non-sexual acts) salvation is by grace through faith and requires repentance. The Corinthians were no longer indulging in sexual immorality. “That is what some of you were.” It is clear, then, that it is possible to have victory over the sin.