Upvote:9
I'm not sure if the Church has an explicit doctrinal position on this question, but I can give you the view of classical philosophy, as originally expounded by Aristotle and then developed chiefly by St. Thomas Aquinas. This view undergirds the thinking of most orthodox Catholic theologians, historically speaking.
In this way of thinking -- assuming you mean non-human animals, the short answer is 'no'.
Classical philosophy identifies three kinds of soul, each with its own distinctive powers:
Plants have vegetative souls1. Most animals have sensitive souls, but human animals have rational souls.
The implication of saying that men have wills and animals don't is that men can, at least in principle, choose what they understand to be good even when it's not what their senses immediately perceive as good. E.g. I can choose to eat my supper before my dessert even when both are sitting in front of me.
Whereas non-human animals are pretty much compelled to pursue the goods that their senses perceive, unless they are directed otherwise by a rational will (e.g.,. a well-trained work animal is largely subject to the will of its owner).
1 Yep, I did indeed say plants have souls. In classical philosophy the "soul" is in general just that which living things have, but non-living things don't have (that's a very informal account).