Garcia cleared waivers Thursday and was sent outright to Triple-A Charlotte, Vinnie Duber of AllCHGO.com reports.
Garcia was DFA'd on Sunday after accumulating a 7.07 ERA and 1.93 WHIP across 14 innings to begin the season. He'll remain in the White Sox organization, but a return to the 40-man roster will likely depend on his ability to turn things around in the minors.