Does a rooster have a penis?

Chickens and roosters just touch to mate that they do not have the "normal" reproductive external organs. So, no, Roosters don't have a penis.

The male chicken (rooster) does not have a penis like other animals and therefore there is no penetration of the female reproductive tract when mating. Instead the female inverts her cloaca (the common junction of the reproductive and digestive systems) which comes in contact with the male's inverted cloaca and receives the sperm. The cloaca is then drawn back into the hen's body and the sperm are captured. They then begin the journey up the length of the reproductive system.