Parker was born in New Orleans, Louisiana, and started his career as a saxophonist, playing with Professor Longhair on his hit "Mardi Gras In New Orleans" in 1949. Over the next decade, he played with most of New Orleans' musicians, including Fats Domino, Irma Thomas, and Huey "Piano" Smith. By 1958, he had started recordingsolo, having a local hit with the instrumental "All Night Long". In 1965 he signed for Nola Records, and had his biggest hit with "Barefootin’". Although he continued to record, he failed to repeat his success in terms of sales, and his recording career effectively ended in the 1970s. However, he continued to perform and tour for many more years, remaining especially popular in the UK.
In April 2007, in recognition of his contributions to Louisiana and national music, Parker was inducted into the Louisiana Music Hall of Fame.