Robinson was born near Greenwood, Mississippi. He left home at the age of 18 and moved to Memphis, Tennessee, where he recorded his first single "Tennessee Woman" in 1957. In 1959, he made his first recording of "As the Years Go Passing By", later recorded by several other blues artists. He settled in Chicago in 1962. He recorded his signature song, "Somebody Loan Me a Dime", in 1967 for the Palos label, the nationwide distribution of which was aborted by a freak snowstorm that hit Chicago. A cover version was recorded by Boz Scaggs in 1969, but the song was misattributed, and legal battles ensued. It has since become a blues standard, being "part of the repertoire of one out of every two blues artists", according to the Encyclopedia of Blues (1997).
Robinson re-recorded the song for the critically acclaimed album Somebody Loan Me a Dime in 1974, the first of three he recorded for Alligator Records. Robinson was nominated for a Grammy Award for the second, 1977's I Hear Some Blues Downstairs, which contained a rerecording of "As the Years Go Passing By".
Robinson played guitar on Larry Davis's original recording of "Texas Flood". Davis later became a guitar player, but for "Texas Flood" Robinson provided the distinctive guitar parts, with Davis on vocals and bass, flamboyant keyboardist James Booker on piano, David Dean on tenor saxophone, and an unknown drummer.
In the 1970s Robinson was arrested and imprisoned for involuntary manslaughter in connection with a car accident. Paroled after nine months, he continued playing in Chicago clubs and later taught guitar.