I, personally believe that is it not a BIRD or a CHIRPING at all.
It would make more sense if the noise was (as I personally believe) the sound of the rocks flying through the air from the trebuchets.
But I 100% agree that the noise is annoying, it is way too loud and the pitch is just irritating. Distracts you from the battle and forces you to focus on it when out of combat.
Please Chivalry Development Team, get rid of the noise or change it.