Beckham will take the roster spot left vacant when left-hander Charlie Leesman was optioned to Triple-A Charlotte after Wednesday's game.
Beckham has not played in a game this season after suffering an oblique injury during spring training. He had made four previous Opening Day starts for the White Sox, but Marcus Semien took his place for the opener this season.
The 27-year-old former first-round draft pick is coming off a 12-game rehabilitation stint with Double-A Birmingham, where he had seven hits in 43 at-bats (.143), with a home run and six RBIs.
Leesman pitched in just one game with the White Sox, starting Tuesday's contest against the Tigers after Chris Sale went on the disabled list with a forearm strain. He gave up six earned runs on nine hits in 2 2/3 innings.