Crockett had his contract purchased from Triple-A Louisville on Thursday.
Crockett will take the place of the struggling Wandy Peralta, who was sent to the minors in a corresponding roster move. The 26-year-old lefty posted a 4.00 ERA and 23:5 K:BB across 27 innings with the Bats before earning a promotion. Crockett will likely be limited to a lower-leverage role out of the bullpen during his time with the Reds.