No. The FBI does not discriminate on the basis of sexual orientation and hasn't since 1994.
Now sexual BEHAVIOR is another thing. Sexual behavior is equally as considered either it be homosexual or heterosexual. Sometimes, sexual behavior can be a concern. For instance, applicants (heterosexual OR homosexual) who engage in unprotected promiscuous sex may be disqualified because it shows a lack of judgement. The FBI actively seeks applicants who are in a stable relationship (be it homosexual OR heterosexual).
If you are in a stable homosexual relationship that does not have a history of sexual dysfunction, (such as an unquenchable continuous desire for sex), then you shouldn't have a problem. Now of course, consenting adults may do what they want behind closed doors, there's nothing wrong with that and that will not disqualify you.
And incase you're about to ask, no homosexuality is not considered a mental disorder by the American Psychological Association so no adverse inference can be drawn from it.
Good Luck!
