After spending four years in the Rangers' minor league system, Vólquez made his Major League debut on August 30, 2005, in a start against the Chicago White Sox. He lost all three Major League games he started that season, as well as one of the three games in which he appeared as a reliever, and posted a 14.21 ERA. He spent the first five months of the 2006 season with the Oklahoma RedHawks of the Class AAA Pacific Coast League until he was recalled to the majors in September. This time, he fared better, winning one of his eight starts and posting a 7.29 ERA.