The veteran wordsmith and the guitarist both share a jet black, gravity-defying hairdo and a similar hollow-cheeked look.
Clarke, 64, told Q magazine that he is confused with the Stones star "all the time" but cannot bear to see the look of disappointment if he admits his real identity.
"Once I was out in Ireland having something to eat and this Norwegian guy sidled up to me and said 'I saw your show in Oslo and you really rock'.
"He thought I was Ron and I can't bear the look of disappointment as it clouds people's features so I just played along with it. He went happily back to Oslo thinking he'd had a drink with a Rolling Stone. Who'd want to shatter that kind of dream?"
Clarke, who said his "official age is 59", also revealed he still writes his poems with a ballpoint pen and does not own a computer.
"Not because I'm a Luddite but because I know how great computers are and I know that if I had one, then you would find me six weeks later dead under a pile of pizza boxes," he said.
"I'm strictly a Biro on the back of a cig-packet writer. If it's good enough for Cole Porter, it's good enough for me."