The oldest versions of the song are posted in this thread by Arkie ("Rounder's Luck") and by Stewie ("Rising Sun Blues"). These date from the 1930s.
John and Alan Lomax published the song, with music, in "Our Singing Country," 1941, under the title "The Rising Sun Blues." The version in the DT is similar, but is one verse shorter.
Lomax obtained the song from Georgia Turner, from Kentucky, in 1937. Some verses he obtained from Bert Morton, also of Kentucky. Lomax notes that a few jazzmen from "before the war have a distant singing acquaintance with the song, indicates that it is fairly old as blues songs go. None of them, however, has information ... about the mother who ran a 'blue-jean shop ...or about the "house they call the Rising Sun." "We have heard it sung only bt southern whites."
Lomax was not a documenter, and seldom looked into the background of the songs that he collected.