Robertson pitched for the silver medal-winning USA team in the Tokyo Olympics.
The right-hander is 53-33 with 137 saves and a 2.90 ERA in 12 major league seasons, including nine with the New York Yankees.
Robertson last appeared in the majors in 2019, pitching in seven games for Philadelphia.
To make room on the 40-man roster, the Rays transferred left-hander Jeffrey Springs from the 15-day to 60-day IL.
Springs underwent surgery Monday to reconstruct a torn ACL in his right knee. The reliever was hurt July 31 against Boston.
Glasnow is out the for the season and likely all of next year as well following Tommy John surgery. Anderson is on a rehab assignment with Durham.