If your degree is anything like mine you won't be programming in C right away - your first papers will be on discrete math, logic, archetecture, assembly, etc. Learning these things first will make it a lot easier to do system programming in C, which is really the whole point.
It would be useful for you to know some simpler high level language though, just to get you used to thinking in loops and functions etc. Perhaps PHP? I assume you know HTML already (If not learn it). Or some kind of shell scripting?
Also if you have never done the following before, and it sounds like something you might enjoy, I would suggest you do it:
Buy a cheap computer off ebay. Something old, crap, maybe slightly exotic, but mostly working. Look it up and find out about the components. Take it apart, clean it up, and put it back together again. Overclock it. Install Linux on it - not one of these new GUI desktop systems but something really basic like minimal debian. Rebuild the kernel. Install some software from source. Network it with your main machine. etc etc...
This stuff is NOT computer science and they will NOT teach you anything like this, but it will be HIGHLY advantagous for you to know it. People expect you to be familiar with this sort of thing. It will open up all sorts of interesting projects to you.