He retired as President of Oklahoma City University in 2018, and has since worked as an attorney specializing in mediation, moot courts, and appellate advocacy.

While attending law school, he was appointed Attorney General for the university student association, and was elected to the Oklahoma House of Representatives, where he served until 1986.

Henry was nominated by President Bill Clinton on February 9, 1994, to a seat on the United States Court of Appeals for the Tenth Circuit vacated by Judge William Judson Holloway Jr.

He was named by United States Supreme Court Chief Justice William Rehnquist as Chair in 2005.

In 2004, he served as part of a six-member delegation, led by Supreme Court Justice Sandra Day O'Connor, which represented the United States Judiciary at the Arab Judicial Forum.

Henry became President Emeritus of Oklahoma City University in 2018, and is now in the private practice of law specializing in mediation and arbitration, conducting moot courts, and consulting on appellate advocacy.

A life member of the National Conference of Commissioners on Uniform State Laws, Henry also has been active in the American Bar Association.