What Happened To Everyone Who Dated Joker?
4. An Unnamed Man - Batman: Devil's Advocate
Although more the subject of fan speculation that any concrete evidence, Batman: Devil's Advocate contains one particularly noteworthy panel, where Batman's interrogation of Gotham's inhabitants leads to one random man claiming that Joker 'broke my heart, then broke my legs'.
While it isn't explicitly said, this sentence suggests pretty heavily that Joker had some kind of a romantic history with this man, before kicking him to the curb like all his love interests.
With debate about this still being rampant years later, it seems only fair to mention that it appears to be at least hinted that the Clown Prince of Crime has dated men in the past - although a diabolical serial killer probably isn't the best person to lead comic's representation of bisexual people.