They didn't have a God of birds.
Faunus
he is god of nature and flocks.
The symbol for the god of nature and flocks is usually depicted as a shepherd's crook or staff, known as a "crook and flail." It represents the god's role as a shepherd or protector of flocks in nature. In ancient Egyptian mythology, the god associated with these symbols is typically depicted as a human figure with the head of a ram or a ram itself.
I believe it is Pan.
The Greek god of shepherds and flocks is Pan. He is often depicted as a half-goat, half-man creature with horns on his head. Pan is also associated with nature, wilderness, and rustic music.
The god of the shepherds and flocks is Pan
Pan is one of the most famous Satyrs. He was god of shepherds, flocks, mountains, hunting and music.
The Greek god Pan. He was the god of flocks/herds/nature and was typically represented as a satyr (half man half goat).
Technically, the Roman goddess Diana was the goddess of nature, as well as of fertility childbirth, wildwood, moon, forests, animals, mountains, woods, women, and the moon. She was variously known as Mother of Creatures, the Huntress or Destroyer, and Goddess of the hunt. However, other gods/goddesses often had specific realms of nature that they governed. For example(s), Ceres was goddess of corn and grain crops; Jupiter was the god of the sky, lightning, and thunder; Neptune was god of the sea and its creatures; and Mars (far from being only "god of war") was also god of spring, growth in nature, and agriculture.
Pan. He was also the god of nature in general. Pan was the Greek god. His Roman counterpart was Faunus.
Pan was the Greek God of shepherds and flocks, somebody misspelled the question.
Saturn was the Roman god of Agriculture and the Harvest, while Ceres was goddess of nature and the fertility of the earth.
He is god of Shepherd's and flocks.