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).

Bancroft served in the 8th New Hampshire Infantry Regiment of the Union Army during the American Civil War.

After recovering, he returned to his regiment and achieved the rank of bugler.

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