While he's known for portraying complex and charismatic characters, his roles have typically been heterosexual. However, he has been praised for portraying characters that defy stereotypical masculinity, like Tyler Durden in "Fight Club", which explores themes of identity and gender roles.
There have been rumors and speculations about his sexuality throughout his career, but he has never publicly identified as gay.
It's important to note that actors can and do play roles that challenge gender norms and stereotypes, regardless of their own sexual orientation.