Rodriguez was reassigned to the Red Sox's minor-league camp Sunday.
Rodriguez, who last appeared in the majors in 2016 with the Athletics, was sidelined for much of the 2017 campaign while recovering from shoulder surgery. The 33-year-old still looked a little rusty in the Grapefruit League with a 9.00 ERA and 1.63 WHIP over eight innings, so he'll need to prove healthy and effective in the upper minors before getting a serious look from the Red Sox.