The White Sox placed Thorpe (elbow) on the 15-day injured list Wednesday.
Thorpe had Tommy John surgery last April and encountered a setback in February when he developed tendinitis in his elbow. He's been throwing off the mound for a few weeks, however, and should be ready for a rehab assignment soon. Still, given the long layoff, Thorpe is a candidate to be shifted to the 60-day IL eventually.