In December 1980, Stein was signed as a free agent by the Texas Rangers. Stein made his Rangers debut on April 14, 1981, against the Cleveland Indians. In that game, he got one hit in two at-bats. In May, Stein set an American League record by recording seven consecutive pinch hits. Through June, Stein had a .441 batting average. On the season, Stein batted .330 with 21 runs scored, 38 hits, six doubles, two home runs, and 22 RBIs in 53 games played. In the field, he played 20 games at first base, seven games at third base, seven games in left field, three games at second base, one game in right field, and one game at shortstop.