The shocking allegation is featured in Call Me Dave: The Unauthorised Biography, written by Michael Ashcroft.
Ashcroft allegedly fell out with Mr Cameron after he claims he was snubbed for a "not insignificant" position.
The founder of the Piers Gaveston Society, Valentine Guinness scoffed at the story as "malicious gossip".
"It is a ridiculous story,' he told The Spectator. "As far as I know David Cameron was never a member of the Piers Gaveston Society, so there would have been no need for an initiation ceremony."
However that didn't stop Twitter users reacting with jokes, puns and a bunch of animated photos.
Under the hashtag "PigGate", one Twitter user said "Fifty Shades of Pork..coming summer 2016...directed by Kermit the Frog."
Others dug out pictures of Cameron on farms in his Oxfordshire constituency holding pigs.
Paul Henry wrote: "David cameron is being owned by the internet."
Another Twitter user wrote: "All this nonsense is enough to make you choke on your bacon sandwich."
Charlie Brooke, an English satirist and broadcaster has also taken to Twitter to say that he has never heard anything about Cameron and a pig after imagining a storyline in which the prime minister gets intimate with a pig his TV series Black Mirror four years ago.