Francis Carter Bancroft (May 9, 1846 – March 30, 1921) was an American manager in Major League Baseball for the Worcester Ruby Legs, Detroit Wolverines, Cleveland Blues, Providence Grays, Indianapolis Hoosiers, and Cincinnati Reds of the National League, as well as the Philadelphia Athletics of the American Association. His greatest success came with the Grays, when he won the 1884 World Series with a record of 84–28 (.750 winning percentage). His stops with teams were short, usually in an interim role, with his last stop being with the Reds after Bid McPhee left the job as manager. Bancroft was 56 years old at the time.
He died in Cincinnati, Ohio at age 74.