Mejia signed a minor-league contract with the White Sox on Tuesday, James Fegan of The Athletic reports.
Mejia was designated for assignment and released by the Angels earlier in the month, but he'll still get a shot to earn a roster spot after being invited to the White Sox's big-league camp. He's not particularly likely to do so, however, as he struggled to a 6.61 ERA and a 14.5 percent walk rate in 31.1 innings for the Twins, Cardinals and Angels last season.