Absolutely! But that is not to say that it will be easy. Indeed, most Christians face some sin in their lives that becomes a battle for them.
Nevertheless, God has made provision for all Christians to have victory over sin. Romans 6, in particular, speaks of the baptised Christian being set free from the power of sin. That applies just as much to homosexuals.
Again, let us be clear: it does not guarantee that it will be easy. It might be an ongoing battle but it is winnable, by the grace of God.
The Bible addresses homosexual behaviour not inclination. Whatever our inclination, behaviour is a choice. We cannot claim that we have been forced to act in any way.
1 Corinthians 10:13
No temptation has overtaken you except what is common to mankind. And God is faithful; he will not let you be tempted beyond what you can bear. But when you are tempted, he will also provide a way out so that you can endure it.
We have a slightly fuller treatment of this in the page entitled “The Gospel Provides An Escape From The Power Of Sin”.