Webb, 25, previously served as the 26th player for the White Sox on April 26 against Kansas City, but he did not pitch.
Webb is 1-1 with a 4.01 ERA, two saves, 21 strikeouts and a .237 opponents average in 15 games with Charlotte this season. The reliever has gone two-plus innings eight times and is limiting right-handed hitters to a .229 mark.
Webb is 6-5 with a 3.87 ERA, five holds, and 68 strikeouts in 66 career relief appearances over two seasons with the White Sox. He will be used out of the bullpen and may have a chance for a save opportunity with David Robertson going two innings Wednesday in Chicago's 5-3 win over Toronto.
"We got a mixed bag today," manager Robin Ventura said. "With Robbie going two yesterday, you are probably not going to use him. We'll see how he's feeling today as he moves around and does stuff. The chance of him going in are probably slim, but you never know."
Webb must stay up for both games of the doubleheader. Between games, the White Sox officially called up No. 12 prospect Chris Beck -- who made his Major League debut in Game 2 on Thursday -- from Triple-A, while optioning righty Scott Carroll.
Connor Smolensky is an associate reporter for MLB.com.