The Prime Minister said he was the thirteenth cousin of the US celebrity, who is married to rapper Kanye West and first became famous after starring in a leaked sex tape.
Asked by Heat magazine whether he watched the television show 'Keeping Up With The Kardashians', featuring Kim and her family, Cameron said: "No, but I'm related to them. Did you know I'm 13th cousins with them?"
The link is via a mutual ancestor, Sir William Spencer, born in 1555, according to genealogy website geni.Com.
Asked what he wanted to be when he was growing up, he said: "All sorts of things: a soldier, a lorry driver, a farmer. I wasn't sure till I left university, then decided I wanted to be a politician."
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The Prime Minister also admitted to an inability to multi-task and a fear of rats.
Asked what tunes he uses to pump up his thrice weekly two-mile runs, he replied: "I'm a man, I can't do two things at once. Don't be ridiculous."
Cameron also said one of the everyday things he misses since becoming Prime Minister is, "You know, putting some music on, driving the car, losing yourself a bit."
Cameron is seeking a second term as Prime Minister and is in the midst of campaigning for elections next month.