In a corresponding move, the White Sox optioned right-hander Nick Padilla to Triple-A Charlotte.
Crochet, 23, underwent ulnar collateral ligament replacement surgery on April 5, 2022. Crochet made six rehab appearances between Charlotte and Double-A Birmingham after starting the season on the IL. He had a 7.50 ERA in six innings.
The 6-foot-6 Crochet is 3-5 with a 2.54 ERA in 59 relief appearances with the White Sox in 2020-21. He was selected No. 11 overall by the club in the 2020 draft.
Padilla allowed two earned runs over two innings in his only appearance with Chicago last week. Padilla has made just two major league appearances.
Crochet's last regular-season game was Oct. 1, 2021. The White Sox will host the Cleveland Guardians on Tuesday.
Information from Reuters was used in this report.