"그럼 사회쭉이야?" => 그럼 사회 쪽이야? (쭉 -> 쪽) == 그러면 사회 쪽이야?
그럼 (그러면, then), 사회 (society, social) 쪽 (direction, side) 이야 (is it?)
Literally it is like "Then is it the society side?" which is not clear in meaning.
It is a heavily elided expression which can only make sense in context of other remarks.
Native speakers can however imagine where such a phrase might be uttered.
Here's one possible scenario:
AA: 나 이번에 XX 대학교에 들어갔어: I just got into XX university.
BB: 그래? 축하한다. 무슨 전공으로?: 정치? Is that right? Congrats. Majoring in what? Politics?
AA: 아니: No.
BB: 그럼 사회 쪽이야?: Is it then the Social (sciences) side?
* One would normally say 사회학 (Social science), but since "major" has already been mentioned, he just says 사회 쪽.