The White Sox traded Banks to the Phillies on Tuesday, Robert Murray of FanSided.com reports.
Banks earned a save against Seattle on Thursday, striking out two batters in one perfect inning.
Banks will serve as an opener in Monday's game in Cleveland, Daryl Van Schouwen of the Chicago Sun-Times reports.
Banks walked two batters and struck out one in two-thirds of an inning Saturday to record his first career save in a 7-6 win over the Twins.
Banks worked in relief in Saturday's 3-0 loss to the Cardinals, covering two innings and striking out four while allowing one earned run on one hit and one walk.
Banks (0-3) allowed four earned runs on five hits and a walk while striking out three to take the loss Friday against the Athletics.
Banks will start for the White Sox on Friday in Oakland, Daryl Van Schouwen of the Chicago Sun-Times reports.
Banks will start Sunday's game against the Red Sox, Vinnie Duber of AllCHGO.com reports.
Banks will serve as the White Sox's opening pitcher for Monday's game against the Rangers, LaMond Pope of the Chicago Tribune reports.
Chicago recalled Banks from Triple-A Charlotte on Sunday, Daryl Van Schouwen of the Chicago Sun-Times reports.