In corresponding moves, the Rangers selected catcher Sandy Leon from Triple-A Round Rock and transferred right-hander Spencer Howard to the 60-day IL (right lat strain).
Garver, 32, is batting .263 with two home runs and six RBIs in six starts this season. He's a career .248 hitter with 65 home runs.
Leon hit .169 in 33 games last season with Cleveland and Minnesota. He's hitting .273 in four games at Round Rock after batting .250 during spring training.