The White Sox purchased Cleto's contract before Monday night's game against Texas.
Right-hander Taylor Thompson was optioned to the minors on Sunday after Chicago relievers gave up 15 runs and 18 hits in just four innings of a 16-3 loss to Minnesota.
The 25-year-old Cleto was 3-0 with 5.91 ERA at Charlotte. He began the season with the White Sox and had a 5.14 ERA in 13 appearances.
''He's been throwing great,'' manager Robin Ventura said. ''I think after (Sunday) you need a bullpen arm, and he's been the best guy down there. They said, by far, he's been throwing the best.''