Not openly. He has engaged in long-term relationships with Reese Witherspoon and now is involved with Taylor Swift. His orientation appears clearly heterosexual. I think he is bisexual
As far as I know, he's dated Kirsten Dunst (2 years off and on) and Jenny Lewis. Before Kirsten, there were rumors that Jake and his good friend Natalie Portman were dating a little, but that was...