Smith, 93, was one of the most influential guitar-players in country and early rock 'n' roll.
He found fame with his 1948 single Guitar Boogie and enjoyed other hits including Feudin' Banjos in 1955.
When the Warner Bros film studio used a cover version and renamed it Dueling Banjos for Deliverance, he sued them and won substantial royalties.
As well as being a musician, Smith also ran a recording studio and record labels and had a successful career as a radio and TV presenter.
The Arthur Smith Show, on WBTV, was syndicated across the US and ran for 32 years.
He was nicknamed Arthur "Guitar Boogie" Smith after the title of his breakthrough tune, which became a hit around the world.
In Liverpool in 1957, a young Paul McCartney played it during his first concert with The Quarrymen, who went on to become The Beatles.
But nerves got the better of McCartney, who made a mess of it. "I was just too frightened," he later said.
"It was too big a moment with everyone looking at the guitar player. I couldn't do it. That's why George was brought in."
Country music guitarist Arthur Smith, best known for the theme tune from the 1972 film Deliverance, has died.