Well, according to this:
http://gallus.tamu.edu/Extension publications/QA.PDF a rooster DOES have a penis.
A: The male mounts the hen from behind and
stands on her back. The penis transfers
semen into the cloaca of the hen. The
cloaca is a common receptacle for the
intestinal tract, the reproductive system
and the urinary system. Spermatozoa are
stored in accessory sex organs in the
female. There, the spermatozoa are nourished
and released over several weeks. So
the rooster does not have to mate with the
hen each time she is to lay an egg to produce
fertile eggs. Fertility only remains
high for about 10 days to 2 weeks before
another mating is needed to increase fertility
of the eggs laid. Egg yolks that have a
germ cell on the surface are ovulated
about every 24 to 26 hours. The spermatozoa
fertilize the germ cell, then the
albumen,or white of the egg is secreted
around the yolk by the reproductive tract.
Then the shell membranes and the shell
are secreted and deposited as the egg
travels down the reproductive tract. The
egg is laid through the cloaca, as mentioned
above. This is the way fertile eggs
are laid by the hen. The hen would still lay
eggs if a rooster were not around, but the
eggs would not be fertile.