There's nuance to each of the terms. Asocial is what I would say an introvert often is; avoids social interaction without necessarily wishing ill, perhaps dislikes being in the company of others. Anti-social behaviour is disruptive to others, perhaps violent.

Maybe it's a US vs British English thing, but I definitely associate "anti-social" with meaning disruptive to society (e.g. Anti-social behaviour orders in the UK [1])

Upon saying that, "asocial" doesn't really sound right to me. I'd probably go with "non-social" or maybe more poetically use "misanthropic".

[1] https://en.wikipedia.org/wiki/Anti-social_behaviour_order