The White Sox optioned Horn to Triple-A Charlotte on Tuesday.
Horn opened spring camp with the Cubs, but he was traded to the White Sox on Feb. 27 and has surrendered one run in five innings since joining the South Siders. The 26-year-old southpaw logged a 4.58 ERA and 1.53 WHIP across 53 frames in Triple-A last season, but a strong start in Charlotte could earn Horn a promotion into what projects to be a relatively weak White Sox bullpen.