After graduating from Antlers High School, Stephenson attended the University of Oklahoma where he earned a degree in petroleum engineering. Following service in the U.S. Army, where he served as an officer, he joined Amerada Petroleum Corporation.

Between 1973 and 1982, he was part-owner and president of privately-held Andover Oil Company. After the sale of Andover, Stephenson co-founded Vintage Petroleum, Inc., where he served as president, chief executive officer, and chairman of the board. The company grew from three employees at start up to more than 750 with operations in four countries and reserves of approximately 500 million barrels. Stephenson is co-founder and chairman of the board of Premier Natural Resources, an independent oil and gas company and partner of Regent Private Capital. He is co-founder and director of Growth Capital Partners, president of Stephenson Investments, Inc., and serves as a board member of AAON, Inc.

Stephenson is a founder of the Sarkeys Energy Center and, through his foundation, has funded the construction of two research facilities at the Research Campus at the University of Oklahoma. He also serves on the board of trustees for the University of Tulsa. Stephenson was inducted into the Tulsa Hall of Fame in 2000. Both he and his wife were honored with the 2002 Tulsa Humanitarian Award.