If you need to get leadership experience you want to put yourself in a position where you're making important and time-sensitive decisions. I'll give you some examples of what I did while in undergrad.
I was the editor of a cultural newsmagazine. I had a staff of about 30 or so people, and I was in charge of all aspects of the paper -- from the editorial content, to the business side, to whatever's left. This particular activity also helped show that I was well-rounded: who'd have guessed that a science major was the editor of a magazine?
If the idea of editing papers scares you, and you want to stick with something in your field -- how about heading up a research team? That was another thing I did. I found a professor who was an advisor, and I did a research project with a couple other students. I was the principle investigator, however, so that gave me somewhat more exposure to leadership duties.
Just a few thoughts. 🙂