Theodore Frank Appleby was an American realtor, insurance agent, banker, and Republican Party politician from Asbury Park, New Jersey who represented Middlesex, Monmouth, and Ocean counties in the United States House of Representatives from 1921 to 1923. He lost re-election in 1922 and won his seat back in 1924 but died before he was sworn into office. He also served as mayor of Asbury Park from 1908 to 1912.