However, the specific sports he plays are never explicitly stated in the book. The only mention of sports is when Holden asks Stradlater to write a composition for him about his roommate's roommate, a football player named Brossard, and Stradlater agrees.
Therefore, we can assume that Stradlater is at least familiar with football and that he might have played it himself. However, we don't know for sure what sports he plays.