Johnson, 24, was not in Chicago's starting lineup, but is available off the bench.
Johnson was Chicago's opening day second baseman and hit .270 with two doubles, three RBIs, eight runs and three stolen bases in 27 games before being optioned to Charlotte on May 14 to work on his defense.
At Charlotte, Johnson batted .315 with 17 doubles, eight homers and 36 RBIs in 78 games.
Johnson, who stole 28 bases with Charlotte, entered the season rated by Baseball America as the No. 4 prospect and fastest baserunner in the White Sox system.