Typicality a graphic designer works in the publishing (books and uncommonly video games) and/or advertisement industries. Designing things like the packaging a video game comes in, corporate and game logos, can even mean the menu screens (games, DVDs and BluRays), as well anything graphic used in advertising (billboards, flyers, web ads, etc.). All Graphic Design degrees I'm aware of focus on this, and a typical college assignment would be something like "design the brochure for the upcoming theater guild projections".
You don't have to be good at drawing for this degree, but it can definitely help (a lot of graphic designer majors end up as illustrators). And any Graphic Design degree will be focused on getting your design portfolio to be the best it can be. Because a GREAT portfolio will open more doors for you than any level of degree you obtain.
Hope this helps.