A native of Cambridge, Massachusetts, Baker was basically a singles hitter who was able to play all positions except catcher, playing mainly as a right fielder for four different teams. He reached the majors in 1921 with the Philadelphia Athletics, spending part of that season with them before moving to the Chicago White Sox (1923-29), Boston Red Sox (1929-30) and Washington Senators (1930). He enjoyed his best years as a member of the White Sox, hitting .363 (89-for-245) in 1925 and .307 (113-for-368) in 1926. His most productive season came in 1927, when he hit .286 in a career-high 147 games and led his team in doubles (35), RBI (83), stolen bases (20) and sacrifice hits (26). He also tied a major league mark by stealing home twice, in the 1st and 9th innings, during a single game against the Cleveland Indians (May 1, 1924).
In a nine-season career, Barrett was a .288 hitter (690-for-2395) with 23 home runs and 328 in 718 games, including 318 runs, 151 doubles, 30 triples, 80 stolen bases, and a .347 on-base percentage. As a pitcher, he posted a 1-0 record in four appearances for the Athletics.
Barrett died in his hometown of Cambridge at the age of 50.