The Rangers selected Festa's contract from Triple-A Round Rock on Sunday.
He'll join the big-league bullpen as a replacement for right-hander Josh Sborz, who was placed on the 15-day injured list due to right shoulder fatigue. After signing a minor-league contract with the Rangers in July, Festa made six appearances for Round Rock and gave up one earned run on six hits and three walks while striking out 13 batters over 8.2 innings.