The Oakland Athletics selected Steinbach in the ninth round of the 1983 Major League Baseball Draft. Steinbach signed with the Athletics, and made his professional debut in the minor leagues. After two years as a third baseman, the Athletics moved Steinbach to catcher, and played him for two years in Class AA of the minor leagues.
Steinbach made his major league debut on September 12, 1986 against the Cleveland Indians when he hit a home run off of Greg Swindell in his first major league at-bat. He went on to be the starting catcher for Athletics' teams that won three straight American League pennants from 1988 to 1990, and the World Series in 1989. After leaving the Athletics following his career year in 1996, he played his last three years with the Minnesota Twins.
He was elected to the American League All-Star team 3 times (1988, 1989 and 1993). His 1988 selection was highly controversial because Steinbach had posted modest numbers in the first half of the season. However, during the game he accounted for both AL runs with a home run and sacrifice fly, and was named the game's MVP.