The White Sox, who have lost 12 of their last 15 games, announced the moves prior to Friday night's game against the Kansas City Royals. The White Sox (30-30) led the American League Central for 47 days before tumbling into fourth place during the recent skid.
Rollins, 37, batted just .221 with two home runs and eight RBIs over 41 games this season, his first with the White Sox. The three-time All-Star and 2007 National League MVP signed a one-year, $2 million deal with the White Sox on Feb. 22.
Anderson, who turns 23 later this month, is hitting .304 with 10 doubles, two triples, four home runs, 20 RBIs, 39 runs scored and 11 stolen bases over 55 games with Triple-A Charlotte this season. The 6-foot-1, 185-pound Anderson leads the International League in hits and multi-hit games (25) and ranks among the leaders in runs scored (second), total bases (tied for fifth, 101) and average (10th).
Anderson, who entered the season ranked by Baseball America as the No. 1 prospect in the White Sox organization, has batted .337 with 31 runs scored over his last 37 games since May 1.
Anderson owns a .301 average with 62 doubles, 26 triples, 19 homers, 127 RBIs, 220 runs scored and 94 steals over four minor league seasons after being selected by the White Sox in the first round (17th overall) of the 2013 draft out of East Central Community College in Decatur, Miss.
Anderson led the Southern League at Double-A Birmingham in 2015 in hits (160), runs scored (79) and stolen bases (49), ranked third in average (.312) and tied for third in triples (12).