After its initial release, Arkham Asylum received downloadable content (DLC) that added new maps to the game's challenge mode, as well as the Joker as a playable character (albeit only on the PlayStation 3 and Return to Arkham versions).
Answers. To play as the Joker you have to download that add-on from the section of add-ons on the Playstation Network for free, and then go to challenge map and select the Joker to play like him. Thats all you have to do.