Rodriguez, 28, is the son of Hall of Fame catcher Ivan Rodriguez.
Dereck Rodriguez appeared in 51 games over three seasons with the San Francisco Giants. He compiled a 12-15 record with a 4.27 ERA before being designated for assignment by the Giants on Aug. 26. He was claimed five days later off waivers by Detroit before recently becoming a free agent.
Rodriguez made his major league debut at Coors Field on May 29, 2018. He allowed four runs, one earned, over 3⅓ innings. He also had an RBI double off Kyle Freeland.
Rodriguez was originally a sixth-round pick by the Minnesota Twins in 2011.