Sosa's contract was selected from Triple-A Charlotte on Thursday.
Sosa has been in the midst of a breakout campaign in Birmingham to begin the season, as he slashed .331/.384/.549 with 14 home runs, 48 RBI and 47 runs over 62 games at the Double-A level. Although the 22-year-old has never played above Double-A, he'll be rewarded with a big-league promotion to provide infield depth for the White Sox after Danny Mendick (knee) was placed on the injured list Thursday.