Born in Lafayette, Louisiana, but raised in Los Angeles, California, Parker first aspired to a career in entertainment at a young age. By the 1950s, Parker had started working on electric guitar with several blues and R&B bands of the time, with his first stint being with Otis Williams and the Charms. Over the next few years, he also played lead guitar with Bo Diddley and toured with Paul Williams, Sam Cooke, Jackie Wilson, LaVern Baker, Clyde McPhatter, and the Everly Brothers. He first recorded, as Bobby Parks, with the Paul Williams band in 1956.

His first solo single, "Blues Get Off My Shoulder", was recorded in 1958, while he was still working primarily with Williams' band. The B-side, "You Got What It Takes", also written by Parker, was later recorded for Motown by Marv Johnson, but with the songwriting credited to Berry Gordy, Gwen Fuqua, and Roquel Davis.

Parker also performed frequently at the Apollo Theater in Harlem, and in the late 1950s toured with Chuck Berry, Buddy Holly, and Little Richard. By the early 1960s, he had settled into living in the Washington, D.C. area and played at blues clubs there after having left Williams' band.

He recorded the single "Watch Your Step" for the V-Tone label in 1961. The song was written by Parker, inspired by Dizzy Gillespie's "Manteca" and Ray Charles' "What'd I Say". It reached no.51 on the Billboard Hot 100 in 1961, although it did not make the national R&B chart. It was later covered by several British acts including the Spencer Davis Group, Dr. Feelgood, Steve Marriott, Adam Faith, and also by Carlos Santana, and was performed by the Beatles in concerts during 1961 and 1962. The song's guitar riff inspired the introduction to the Beatles' 1964 hit single "I Feel Fine", and, according to John Lennon, also provided the basis for "Day Tripper". In relation to the Beatles' use of the riff, Parker said: "I was flattered, I thought it was a cool idea. But I still had, back of my mind, that I should have gotten a little more recognition for that." Led Zeppelin also used the riff as the basis for their instrumental "Moby Dick".

With the success of the song, both in the United States and overseas, he toured the UK in 1968 and recorded his next single, "It's Hard But It's Fair" produced by Mike Vernon and released on Blue Horizon. Jimmy Page was a fan of the obscure bluesman and several years later, in the mid-seventies, wanted to sign Parker to Swan Song Records. Page offered an advance of US$2000 to fund the recording of a demo tape, but Parker never completed the recording, and an opportunity for Parker to be exposed to an international audience was lost. On January 1, 2012, Parker's "Watch Your Step" sound recording became Public Domain in Europe, due to the 50 year copyright law limit in the E.U.

For the next two decades, Parker played almost exclusively in the D.C. area. By the 1990s, he started to record again for a broader audience. He recorded his first official album, Bent Out of Shape, for the Black Top Records label in 1993, with a follow-up in 1995, Shine Me Up. In 1993, he also was the headliner for the Jersey Shore Jazz and Blues Festival. Parker continued to perform as a regular act at Madam's Organ Blues Bar in Washington.

Bobby Parker died of a heart attack on October 31, 2013, at the age of 76