It was first published in 1913 by the blind Richard Burnett. Also recorded by the Stanley Brothers and others.
Played by Bob Dylan on Bob Dylan (1962).
The song appears in the film performed by the fictitious Soggy Bottom Boys, but it was actually recorded by Dan Tyminski, Harley Allen, and Pat Enright.
So, the voices behind the Soggy Bottom Boys were well-known bluegrass musicians: Union Station's Dan Tyminski (lead on "Man of Constant Sorrow"), Nashville songwriter Harley Allen, and the Nashville Bluegrass Band's Pat Enright.
Chris Thomas King played the guitar in the version at the recording studio. Tim Blake Nelson (who played Delmar) sang the lead for 'In the Jailhouse Now' himself.