Born in 1850 at Newstead in Christian County, Kentucky, his family moved to Louisville in 1856, and young Barker received his primary education in the public schools of that city. From 1869 until 1872 he attended the Agricultural and Mechanical College of Kentucky, but withdrew from school in order to pursue a career in the legal profession. Admitted to the bar in 1873, he began the private practice of law. Barker was married on May 22, 1886 to Kate Sharp Meriwether, of Clarksville, Tennessee; they had no children. In 1887 he was elected Louisville City Attorney, a post in which he served until 1896. Associated for a time with his brother, Maxwell S. Barker and later affiliated with the law firm of Kohn and Barker, he was elected Judge of the Jefferson Circuit Court (Criminal Division) in 1897 and in 1902, Judge of the State Court of Appeals. He served the last year of his term as Chief Justice of the Court. In 1910 he was elected President of State University by the trustees of the school; his term of office began on January 1 of the following year.
The Barker administration was plagued with troubles from the start, as Patterson did not willingly relinquish the powers of the position he had held for forty years. Openly and actively opposing the selection of Barker as his successor, ostensibly on grounds of lack of education and experience, the aging former president and his allies hounded him continually and relentlessly throughout his brief term of office.
The Barker administration, despite organized opposition of the sort, could nevertheless point to significant accomplishments. The Graduate School, Department of Journalism and Y.M.C.A.were established on campus during his administration, and the Reserve Officers Training Corps was set up in 1917 to provide instruction for military personnel participating in the World War the United States had recently entered. The College of Law, founded in the last years of the previous administration, grew appreciably. The University's newly established library increased significantly in size and stature, and the first printing press on campus was procured at Barker's own expense. Agriculture and the University's role in its promotion and nurture throughout the state were emphasized by the Barker administration. The College of Agriculture, long neglected by Patterson, increased in size and significance, a development marked by the enlargement and expansion of the Agricultural Experiment Station. The College's constituent School of Home Economics experienced substantial growth, assuming a place of regional leadership in its field. This enhancement of some of the University's major programs, coupled with the good will engendered largely as a result of the extension of its activities in the field of Agriculture among its statewide public constituency, resulted in a dramatic, nearly twofold increase in University enrollment during Barker's term. In March, 1916, the State Legislature statutorily changed the name of the growing institution from "State University, Lexington, Kentucky" to "University of Kentucky".
Student activities likewise thrived and increased in the relatively democratic campus atmosphere Barker created. In enforced residence on the campus in Patterson Hall Dormitory, away from the "President's House" (which Patterson intransigently occupied until his death in 1922), Barker appeared especially attentive to the interests and concerns of his students. The student newspaper of the time -The Idea and its successor, the Kentucky Kernel (introduced in the fall of 1915) were published weekly and attracted a broad and active readership. Student government had its origins in the Student Self- Government Organization founded in 1912. Moreover, Barker, a proponent of physical training, encouraged student participation in athletics, and basketball and football in particular flourished during his tenure.
The Patterson faction's opposition to Barker's presidency came to a head in 1917 with opposition by the Board of Trustees and interested academic leaders to his attempt to merge three of the University's Engineering programs. An investigation of the President was conducted, which led to his resignation. Barker returned to Louisville and established a successful law practice. Reentering politics, he ran for and was elected Circuit Judge. He died suddenly on April 23, 1928, while visiting a cousin in Jeffersonville, Indiana.