Applies as a nickname to a male with a penis that bends to one side, or is not straight when erect. This term is especially useful for any of your friends with the name "Ben," where "tweiner" follows as their make-believe last name. It yields a hilarious nickname that sounds just like "bent weiner."
I heard through the grapevine that you've got a tweiner!
Friend: Sup' Tweiner?
Ben: Shut up, ass-hole.