Asked by Heat magazine whether he watched the television show Keeping Up With The Kardashians, featuring Kim and her family, Mr Cameron volunteered: "No, but I'm related to them.
The link is via a mutual ancestor, Sir William Spencer, born in 1555, according to genealogy website geni.com.
Among other disclosures in the interview, the Eton-educated Prime Minister claimed he once aspired to be a lorry driver.
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 til I left university, then decided I wanted to be a politician."
The Prime Minister also admitted to an inability to multi-task and a fear of rats.