Rock Me Baby is a song written by BB King, it was BB's 1st top 40 hit. 
BB and Muddy Waters both had hits with Rock Me Baby using a song that was originally recorded by Lil' Son Jackson titled Rockin and Rollin as the basis of their recording.
Over the years, many blues and other artists have interpreted and recorded "Rock Me Baby" and it has become a blues standard. Although Lil' Son Jackson's 1951 "Rockin' and Rollin'" serves as the basis for many versions, B.B. King's and Muddy Waters' renditions are credited for making it well-known.