Raglin started out on guitar but had picked up bass by the mid-1930s. He played with Eugene Coy from 1938 to 1941 in Oregon, and then joined Duke Ellington's Orchestra, where he replaced Jimmy Blanton. Raglin remained in Ellington's employ from 1941 to 1945.
After leaving Ellington's orchestra, Raglin led his own quartet, and also played with Dave Rivera, Ella Fitzgerald, and Al Hibbler. He briefly returned to perform with Ellington in 1946 and 1955. Raglin fell ill in the late 1940s and quit performing; he died in 1955 at age 38. He never recorded as a leader.