Born in Martinsburg, West Virginia, Baker established a legal practice in Cleveland after graduating from Washington and Lee University School of Law. He became progressive Democratic ally of Mayor Tom L. Johnson. Baker served as city solicitor of Cleveland from 1901 to 1909 before taking office as mayor in 1912. As mayor, he sought public transit reform, hospital improvement, and city beautification. Baker supported Woodrow Wilson at the 1912 Democratic National Convention, helping Wilson win the votes of the Ohio delegation. After leaving office, Baker accepted appointment as Secretary of War under President Wilson. He was one of several prominent Georgists appointed to positions in the Wilson Cabinet.