The White Sox recalled Iriarte from Double-A Birmingham on Sunday.
Iriarte started in 22 of his 23 appearances with Birmingham and posted a 3.71 ERA and 1.28 WHIP in 126 innings, but he's likely to begin his big-league career as a member of the bullpen. Expect the 22-year-old right-hander to be deployed mostly in lower-leverage situations initially.