Rodriguez signed a minor-league deal with the Padres on Monday, Brandon Warne of ZoneCoverage.com reports.
Rodriguez spent most of his 2018 season in Double-A, where he posted a 4.26 ERA with 19 strikeouts in 25.1 frames. He last pitched in the big leagues during the 2015 campaign, and although he found decent success (3.86 ERA over 14 innings), he hasn't managed to return since. After he was released by the Twins in August of last year, Rodriguez figures to serve as organizational depth for San Diego.