What has the joker done to be called a villain?

Answer 1

No. The Joker is considered to be a supervillain, and not an anti-hero. He is full of pure, psychotic evilness as opposed to an anti-hero, who would just do things for their own benefit that tend to be evil.

Answer 2

He's murdered countless people, Psychologically and chemically tortured others, stolen from numerous banks and factories, broken in and out of every type of building imaginable and wears a skintight bathing suit when swimming.