Barker was born in Muskogee, Oklahoma on June 20, 1935. He graduated from the Oklahoma Military Academy and went on to earn a degree in business administration from Northeastern Oklahoma State University in 1957. From 1957 to 1959 Barker served as a first lieutenant in the U.S. Army's First Infantry Division, commanding a tank battalion. Following his military service Barker founded Muskogee Restaurant Supply and was president of that company throughout his career in politics. He was married to the former Kay Tucker, and had two children, Janet and Brad.
Barker was first elected to one term in the Oklahoma House in 1968, and was later elected for seven more terms, from 1977 to 1990. He served District 13, which covers Muskogee and parts of Muskogee County. As a member of the House, Barker had a seat on the Appropriations and Budget Committee and was vice-chairman for four years. He also served on the joint House-Senate General Conference Committee on Appropriations.
In 1983 Barker was elected as Speaker of the House after a federal felony conviction forced the previous Speaker, Dan Draper, to leave office. His tenure as Speaker coincided with a difficult period in Oklahoma history as energy prices collapsed, state revenues were in shortage, and the Democratic legislature was often at odds with the Republican governor, Henry Bellmon. It was a period marked by efforts toward government reform, tax increases, revenue restructuring, and economic development. Despite these challenges, Barker was generally regarded by Democrats and Republicans alike to be a strong and effective leader.
On May 17, 1989, Democratic members of the House voted for Barker's removal as Speaker, citing a need for a change in leadership and policies to match the changing times, as well as disapproval of Barker's majority floor leader, Guy Davis. Barker's composure during the ouster proceedings and the personal respect he had achieved among his colleagues earned him a standing ovation as he left the House chamber that day. Barker served the remainder of his term but declined to run for reelection in 1990. After leaving the House, Barker moved to Edmond, Oklahoma and became a lobbyist, representing banks, the insurance industry, and advocates against domestic violence. Barker died of a stroke on April 25, 2005, at the age of 69.