Valerie and Ted Rock took him in two years ago after visiting a bar near their home in Chicago, where he was being passed round by curious drinkers.
He was one of a large litter and the owners were looking for a home for him.
Yoda's extra 'flaps' are separate to the base of his skull, with one placed slightly behind the other.
Yet despite his unusual looks, Valerie is sure Yoda's behaviour - and hearing - are quite normal.
'Yoda's hearing is normal as far as we know,' says Valerie. 'People do a double take when they see him or his picture. It is great fun showing him off.
More details here.