Scott was born in Pocatello, Idaho, to Kenneth Leroy Scott and Mary Eliza Whittle. When he was five years old, the family moved to Washington, D.C., where his father worked in the U.S. Department of Agriculture. His father was not a member of the LDS Church at the time, and his mother was marginally active, until the U.S. Secretary of Agriculture in the Eisenhower administration, church apostle Ezra Taft Benson, named Kenneth Scott as Assistant Secretary of Agriculture. Benson's influence led to his father's conversion and the reactivation of his mother. In 1988, as church president, Benson appointed Richard as a church apostle.