The Rangers selected Kennedy's contract from Triple-A Round Rock on Tuesday.
The veteran right-hander made the Rangers' Opening Day roster as a non-roster invitee, but he was designated for assignment and elected free agency in mid-May after he posted a 7.20 ERA in 11 outings. Kennedy re-signed on a minor-league deal in June and has a 3.51 ERA and 30:9 K:BB over 25.2 innings at Triple-A, and he'll receive another chance with the big club for the stretch run.