Oh yeah, you can. I'm going to be a soph in high school, and I have the brochure for it. If you want to apply for the studying abroad program, here's the link: www.yonsei.ac.kr/eng/intro/exchangeuniv.html
If you want to e-mail them... then you can PM me.

Fall 2006 admissions were already due, but you can apply for the Spring 2007 Admission, which the apps are due somewhere between July 14, 2006 and September 15, 2006. No, there are a lot of foreign exchange students. Well, actually, half and half. This is for the studying abroad one though.
Actually, Yonsei's not as difficult to get in compared to Harvard. My cousin who lives in Korea, applied for American universities because they're "better." He got accepted into Brown Uni, NorthWestern Uni, and some other Ivy Leagues. So don't worry too much. It's easier to be accepted into Yonsei if you're not a Korean citizen, but you've got to have the grades and achievements.
I was going to go, but my parents are sending me to a Leadership program in Washington D.C., so this will have to wait until next year. :]
Hope that helps. Bye<3