Martinez hit .239/.329/.388 with 10 RBIs for Tampa Bay this season, and owns .946 OPS for his career against left-handed pitching.
The 32-year-old owns a career slash line of .294/.361/.455 with 43 home runs and 182 RBIs. He's owed the prorated portion of his $2-million salary for this season and isn't eligible for free agency until 2023.
Martinez spent four seasons in the NL Central with the St. Louis Cardinals before they traded him to the Rays in January.
Chicago designated catcher Josh Phegley for assignment to make room on the active roster for Martinez.