The closest we get is the scene in the animated film "Batman: The Killing Joke" where Joker attempts to convince Batman that he's just a "bad day" away from becoming a criminal. This scene is meant to illustrate the Joker's philosophy that anyone can be pushed over the edge, but it doesn't involve a joke per se.
The idea of the Joker making Batman laugh is more of a thematic concept than a literal event. It represents the Joker's chaotic and nihilistic view of the world, contrasting sharply with Batman's order and justice.
So while it's a fun thought, there's no actual instance of the Joker telling a joke that makes Batman laugh in the canon.