The Beatles had just released their first movie A Hard Days Night and broken big time in the US - with the top five singles at one time in the American charts.
However, the car was believed to be ideal for a band member - with its huge V8 engine making light work of long motorway runs.
The Chassis HK2 B160, bought new by Ringo, was the very last of only 26 right hand drive Facel II's ever produced.
It was delivered to Ringo's home in Weybridge, Surrey, and he owned the car for four years.
Now, it is set to sell for between £300,000 and £350,000 at Bonhams auction house in New Bond Street, London, on Sunday, December 1.
The French firm of Facel produced about 2,900 hand built cars during its few years of existence - all of which were stylish, luxurious and fast.
Launched in 1961, the Facel II was priced in Rolls-Royce territory - with only 182 models ever built.
It was bought by the rich and famous seeking something exclusive and distinctive, including Tony Curtis, Danny Kaye, Joan Fontaine and Ava Gardner.
It was also favoured by great motor racing figures such as Sir Stirling Moss.
The vehicle was destined to be the last of the V8-engined models - with production ceasing in 1964 after an unsuccessful venture into engine manufacture effectively bankrupted the company.
Sholto Gilbertson, collectors car director at Bonhams, said: 'This car has to be one of the rarest and most collectable modern classic cars given its almost unique engineering and its place as part of pop music history.
'As Ringo drove this car he would have listened on the car radio to the Beatles total domination of the pop charts.
'The sale of this car represents a once in a lifetime opportunity for anyone who loves cars and the Beatles.'
By Sophie Jane Evans