Charles Sidney Baxter (August 27, 1866 – January 18, 1927) was an American politician who served as mayor of Medford, Massachusetts.

He graduated from The English High School in 1883 and went to work as a stenographer for the Metropolitan Street Railway.

He also served as an attorney for the Grand Trunk Railway during its effort to enter Boston.

Frothingham defeated John N. Cole and Robert Luce for the Republican nomination, but lost to Eugene Foss in the general election.

In 1915 he managed Samuel W. McCall's victory over incumbent David I. Walsh in the gubernatorial election.