"overacting inferior performer," 1882, American English, apparently a shortening of hamfatter (1880) "actor of low grade," which is said (at least since 1889) to be from the old minstrel show song, "The Ham-fat Man" (attested by 1856). The song, a comical black-face number, has nothing to do with acting, but the connection might be with the quality of acting in minstrel shows, where the song was popular (compare the definition of hambone in the 1942 "American Thesaurus of Slang," "unconvincing blackface dialectician"). Its most popular aspect was the chorus and the performance of the line "Hoochee, kouchee, kouchee, says the ham fat man."
Ham also had a sports slang sense of "incompetent pugilist" (1888), perhaps from the notion in ham-fisted. The notion of "amateurish" led to the sense of "amateur radio operator" (1919).