From a TDKR tie-in book, regarding Joker's possible origins:
The report suggests that since many of Joker's henchmen were former patients of Arkham Asylum that maybe he was one, too, but they'd yet to find any record of him there.
The Joker does not appear to have any connections to Gotham's crime syndicates, though he knocked over a mob bank. One possible motive for this, which could also explain the clown motif, is the Haley Brothers Circus. The circus was recently in town for a two-month engagement and it was rumored their boss had connections to Sal Maroni. The Joker could be a former Haley Brothers employee with some kind of grudge against the mob.
Given the Joker's access to, and relative comfort with, military-grade technology such as grapple cannons, weaponized gases, explosives, and automatic weapons, it is possible that the man is a former soldier, perhaps suffering from severe PTSD. The Joker has murdered or attempted to murder various civic officials. It is possible that he is an extremist anti-government agitator or a soldier angry with the government for sending him to war.