Well, not as such, but the entire institution was deliberately started right next to Scripps Institute of Ocenography (right up the hill from Scripps--2 min drive), and many of the faculty at Scripps are also faculty at UCSD. The two institutions are intertwined vis a vis research/teaching.
EDIT: Even in this era of decline in support for higher education i would never try to discourage anyone from going to any of the UCs. Don't get the idea I'm trying to discourage you--maybe I didn't make it all that clear--I don't think UCSD offers a specific undergraduate program in marine science--I really don't know of any universities that do (maybe this has changed, you'd want to look at their web site and see what they offer)--rather, you would major in one of the major sciences, depending on your interest--you mentioned biology, so lets say you majored in biology or biochemistry or bioinformatics, molecular biology, genetics, whatever--then specialize in the marine aspect as a graduate student at Scripps. Check out their site, maybe call them up and see what's available. San Diego was a great place to grow up and go to school, but it's a different place now, at present it's only great if you've got plenty of money, otherwise the only positives are the weather and the ocean. Of course if you're a student it's always simpler, since you'd only have to worry about yourself, and you can get by for a lot less. Fees are gonna really bite, though...and if you're not a state resident there'd be tuition on top of that...
EDIT: Even in this era of decline in support for higher education i would never try to discourage anyone from going to any of the UCs. Don't get the idea I'm trying to discourage you--maybe I didn't make it all that clear--I don't think UCSD offers a specific undergraduate program in marine science--I really don't know of any universities that do (maybe this has changed, you'd want to look at their web site and see what they offer)--rather, you would major in one of the major sciences, depending on your interest--you mentioned biology, so lets say you majored in biology or biochemistry or bioinformatics, molecular biology, genetics, whatever--then specialize in the marine aspect as a graduate student at Scripps. Check out their site, maybe call them up and see what's available. San Diego was a great place to grow up and go to school, but it's a different place now, at present it's only great if you've got plenty of money, otherwise the only positives are the weather and the ocean. Of course if you're a student it's always simpler, since you'd only have to worry about yourself, and you can get by for a lot less. Fees are gonna really bite, though...and if you're not a state resident there'd be tuition on top of that...