According to one source, he does, and he paid a large sum to prevent it from leaking.
Kim Kardashian's original claim to fame was her sex tape with one William Ray "J" Norwood. Now, according to Radar Online, her husband Kanye West is sitting on a sex tape of his own, and he has paid a large sum to prevent it from leaking,
Radar claims they obtained the information -- "buried in secret court documents" -- that the tape is real. The alleged 20-minute tape features Kanye engaging in sexual intercourse with an 18-year-old woman, who, according to Radar, is a Kim Kardashian-lookalike. The tape was (allegedly) made before Kanye and Kim got together in 2012.
Given the lack of evidence presented by Radar, one is naturally skeptical that a Kanye West sex tape exists. If it is leaked, it will break the internet. We will keep you posted if more concrete evidence emerges.