There are tons of clubs so you can try to become an officer at one that interests you. Besides clubs, UCSD has student body positions that you can run for similar to high school but it’s not a popularity contest and they are not as visible on campus unless you are involved in a student organization yourself. I think this is mainly due to the fact that the campus is very large and there are a large number of students.

You will find plenty of opportunities because there are so many different organizations. The key is to go out there yourself and find one that interests you. If you can’t find one, you have the option of starting one yourself.