Thompson is the son of former NBA player Mychal Thompson and the brother of Golden State Warriors lottery pick Klay Thompson. His older brothers, Mychel and Klay, also played college basketball. Klay Thompson is currently a shooting guard for the Golden State Warriors. His mother, Julie, played volleyball at the University of San Francisco.
Thompson starred at Santa Margarita Catholic High School in Rancho Santa Margarita, California. He was drafted by the Chicago White Sox in the second round of Major League Baseball's June 2009 amateur draft. He spent the 2009 season playing for the Bristol White Sox and Great Falls Voyagers in the rookie leagues.
With the 2013 Birmingham Barons, Thompson batted .229 with 78 runs on 116 hits, 15 home runs, 73 RBI, 25 steals
- Wray, Cheryl (April 13, 2014) "Going his own way: In a family of basketball players, Birmingham Baron Trayce Thompson chose baseball." The Birmingham News
- Trayce Thompson at baseball-reference.com