I get why some people would be taken aback to the idea of Joker being a rapist, but I don't see it as being entirely out of the question for the character.
1.) We do see Selina Kyle beaten and hogtied in Dark Knight Returns, plus he uses the mind control lipstick on her and she warns Batman not to let Carrie near him and that he's "worse than ever"
2.) He rapes Johnny's ex-wife in Azzarello's Joker (that **** ain't implied, he legit comes out of the car with his pants undone while she appears traumatized in a fetal position and he tells Croc to pay her for "whatever it was worth" , c'mon y'all)
3.) He's rather sexually provocative in Arkham Asylum ASHOSE to the point where he grabs Batman's ass, asks if Robin "started shaving yet" , and in his diary he writes " fill the streets with murder and rape! Let there be Ecstacy, ECSTACY in the streets ! "
4.) Even in Batman 89/TDK he's rather forceful on both Vicki Vale and Rachel. " A little fight in you... I like that. "
5.) If we're willing to accept the idea of Joker being mentally and physically abusive to Harley... Is it really too much of a stretch to think that there might be some sexual abuse involved too?
So no, I don't see it as being out of the question for him, especially for a character who's supposed to be the most evil Batman villain possible, pretty much the Devil himself. Rape is a form of degradation/humiliation and torture, all of which are right up Joker's alley.