Rodriguez's contract was selected from Triple-A Lehigh Valley on Saturday.
The 24-year-old southpaw posted an impressive 2.35 ERA and 1.15 WHIP while fanning 69 over 76.2 innings between three levels of the minors this year. He will work in low-leverage spots over the final three weeks of the season and could earn a permanent spot in the big league bullpen in 2017.