At the University level, in the US, "what is your major" is the more commonly used phrase (i.e.; I'm majoring in Anthropology and minoring in Linguistics). "What do you study" tends to bring on a list of interests or current classes (i.e.; "I'm taking polisci, English 110, Math 111, Comm 122, and Underwater Basketweaving).
Based on Paul's comment, it seems like it depends on whether you are in the UK or the US.
Hope this helps!