Cleavinger was recalled from Triple-A Oklahoma City on Friday.
The 28-year-old was demoted to Triple-A at the start of May but will return to the majors with Clayton Kershaw (hip) landing on the injured list. Cleavinger had a 3.00 ERA, 1.78 WHIP and 21:12 K:BB over 18 innings for the Dodgers in 2021, and he's allowed one run over 1.2 frames through two outings this season.