In a corresponding roster move, the club has optioned pitcher Edgar Navarro to Triple-A Charlotte.
Santos, in his first season with the White Sox, has a 2-0 record in 47 appearances, with a 2.75 ERA and a 1.28 WHIP. He has struck out 52 batters in 52.1 innings of work for the South Siders.
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His career ERA now stands at 3.57 in 52 games.
Navarro made his MLB debut on July 30 against the Cleveland Guardians. He has appeared in two games for the White sox, allowing two earned runs in three innings. He also has five strikeouts and a walk in those outings.
The White Sox, winners of three games in a row, will take on the Yankees at Guaranteed Rate Field on Tuesday night, with Touki Toussaint taking on Clarke Schmidt.