Shaw was born in Brenham, Texas, United States.[1] He was taught to play both the harmonica and guitar by his relatives, and based his style on his collaborations with Blind Lemon Jefferson, J. T. Smith and Ramblin' Thomas.[2] After spending time as an itinerant musician in Texas, in 1934 he relocated to California.[2] He continued to perform and appeared on radio, before setting up his own club which he operated for many years.[2] By the 1960s, Shaw had been ordained as a minister in a church in San Diego, California, and found a rediscovery of his own during the blues revival.[1]
In the 1960s and 1970s, he recorded for the Advent, Blue Goose and Blues Beacon labels. In addition, Shaw appeared at festivals and, in 1972, he toured in Europe.[1] He recorded "Hey Mr. Nixon" and "Martin Luther King".[3]
Shaw died during open heart surgery in San Diego, in February 1977, aged 69.[3]