He was a lineal descendant of Edward Randolph of the Bremo Plantation, who was his great-great-great grandfather and Benjamin Harrison V, a paternal ancestor who signed the Declaration of Independence.
He attended the University of Virginia, graduating in 1892 with a Master of Arts degree, and continued graduate study there from 1892 through 1895 while also serving as an instructor in mathematics.
During this time he also served as the organist in the University of Virginia Chapel and directed the Virginia Glee Club, leading the latter organization on tours through the Southeast.
Randolph had been elected of the President of the University of Arkansas in 1892, but declined the position.
In 1895, he was elected chair of Mathematics at the University of Arkansas, remaining there until 1897.