Call him a c*** show host ... TMZ has learned, Johnny Carson recorded a sex tape with his wife back in the 1970s -- and not only has the tape just hit the market ... very solid sources tell TMZ, Johnny's johnny is ENORMOUS.

Multiple sources tell us, the tape owner approached the Carson estate in September to make a deal for the footage -- the estate said take a hike, and threatened to sue the owner if he ever sold it.

But the owner's apparently gone rogue -- we're told he's now shopping it to private collectors ... and it is legendary.

According to sources who've seen it, the tape appears to be one of his wives -- it's unclear which one. The tape opens with a naked dark-haired Carson masturbating by a pool -- then shows the woman (with a bouffant hairdo) going all Linda Lovelace.

It goes on for about 5 minutes -- then we're told it cuts to a 20-minute sex scene in Johnny's bedroom ... and Johnny does NOT hold back.

Oh yeah, we're also told he's hung like a horse -- seriously, porn star status. One source said it was at least 10 inches. But for legal reasons it can't go to a porn company, so the only way to unload it is with a private collector.