Schenck was born in Franklin, Ohio to William Cortenus Schenck (1773–1821) and Elizabeth Rogers (1776–1853). William Schenck was descended from a prominent Dutch family and was born in Monmouth County, New Jersey. William Schenck was a land speculator and an important early settler of Ohio who had also been in the War of 1812 and, like his son, rose to the rank of general. He died when Robert was only twelve and the boy was put under the guardianship of General James Findlay.