Trees and power lines were knocked down and several homes near campus were damaged, but no injuries were reported, authorities said.
A spotter reported the tornado in Clemson at 2:56 p.m., about 15 minutes after a tornado warning was issued, according to the National Weather Service.
The worst of the damage happened near Clemson University's football stadium and not far from the downtown area, Pickens County Emergency Management Director Don Evett said.
"It's been raining all afternoon and the warnings were out for a while, so word had gotten out about the storms," Evett said.
The storm also knocked some trees on top of cars on Clemson's campus, university spokeswoman Robin Denny said.
The long warning time from the weather service allowed officials to sound emergency sirens on campus and send out urgent e-mails and text messages to students and faculty, Denny said.
The western half of South Carolina was under a tornado watch for much of Tuesday, and multiple warnings have been issued as bands of storms from the remnants of Tropical Storm Fay moved across South Carolina. The storms were expected to continue through Wednesday.
Fay's remnants were also bringing heavy rain to a large part of the state. Flash flood warnings were issued, and up to five inches of rain had fallen in Lancaster County, authorities said.
Nearly two inches fell Monday at the Columbia airport, with almost 1 1/2 inches falling in just over 30 minutes, according to the weather service.
The rains are welcome as much of the state remains in a serious drought.