Considering the Joker is an anarchist and a crazed killer, with a taste for manipulation (with violence purposes) - I'd say a chaotic evil demagogue bard would fit.
As with Batman himself, the Joker's abilities and skills vary wildly depending on the iteration. If you choose a specific Joker, it will help the process significantly.
CE Alchemist (maybe using the Vivisectionist archetype, you want to play the knife angle more than the poisonous gas angle) would probably be my choice.
We were just talking about this (because of one of my group's awesome Halloween costume) and I was thinking Bard/Rogue/Assassin. But Bard/Alchemist/Assassin might work even better.