Written and originally recorded by Arthur Alexander (US #24 1962).
Other hit versions by The Rolling Stones (UK EP #1 1964), Billy “Crash” Craddock (C&W #37 1972).
From the wiki: “Arthur Alexander is the only songwriter whose songs have been covered by the Beatles (‘Anna (Go to Him)‘), the Rolling Stones (‘You Better Move On’), and Bob Dylan (who recorded ‘Sally Sue Brown’ on his 1988 LP Down in the Groove). Elvis Presley also covered Alexander’s original recording of ‘Burning Love‘ in 1972.
“The Rolling Stones EP was released in 1964 both to capitalize on the group’s first UK Top 20 hit, the Lennon-McCartney-composed ‘I Wanna Be Your Man‘, and to test the commercial appeal of the band before their UK label Decca Records would commit to letting them record an album. Despite the rawness of the production, the EP reached #1 in the UK EP charts in February 1964.”
The Rolling Stones, “You Better Move On” original single release (1964):
Billy “Crash” Craddock, “You Better Move On” (1972):