Arthur Robinson was admitted to the bar in 1910 and began practicing law in Indianapolis. He served in the Indiana Senate from 1914 to 1918 before serving as a first lieutenant, captain, and major in the United Stated Army in World War I.
Following his service in the war, Robinson resumed practicing law and served as the judge of the Marion Superior Court in 1921 and 1922. In 1925 he was appointed to the United States Senate and served until 1935. While in office, he served as chairman for the Committee on Pensions. After his service on Capitol Hill, Robinson practiced law until his death.