The White Sox optioned Peralta to Triple-A Charlotte on Thursday.
After being recalled from Charlotte on Monday, Peralta made a pair of appearances out of the Chicago bullpen, giving up three earned runs on five hits and one walk while striking out three over 4.1 innings. He'll head back to the minors and cede his spot on the 26-man active roster to right-hander Nick Nastrini, who was called up from Triple-A ahead of his scheduled start Thursday versus the Rangers.