Randolph went to school in Pasadena, California, and Little Rock, Arkansas, before coming to Woodrow Wilson High School in Dallas as a junior. Playing for Pat Washington at Woodrow Wilson, he averaged 25.8 points per game and 12.6 rebounds as a senior. He was named to the first team All-Area Dallas Morning News boys basketball team and had 21 points in the 2007 Roundball Classic in Chicago.

Randolph made an impact on the court immediately, as he had six blocks in just the third game of his freshman season. He was the only LSU Tiger to start all 31 games. Although the team ended up with a 13-18 record, Randolph finished strong, averaging 20.1 points during the last nine games.