Randall was born in Gering, Nebraska, the son of horse trainer George Randall, Sr. He was diagnosed with polio as a child, and his father made him exercise in place of the prescribed treatments of the day. By the age of 10, Corky was galloping thoroughbred colts for his father each morning before school. Randall was the recipient of two PATSY Awards and the 1982 Humanitarian Award from the Los Angeles chapter of the Society for the Prevention of Cruelty to Animals. He died of cancer in Newhall, California, at the age of 80.