I think he's an antisocial personality, like all criminals, but I'm not sure about sociopath. Sociopaths can't feel guilt or remorse. Tony has shown guilt and pity on some occasions. He's angry, violent, and has no impulse control, but I think he does have at least a little bit of a conscience.

Richard Kuklinski is a good example of a true sociopath. It never even occurred to him that he should feel guilty over the things he did. He never gave it a second thought.