This is from earlier praeheda, literally "something seized before," from PIE *prai-heda-; for the first element see prae-; the second element is related to the second element in prehendere "to grasp, seize," from PIE root *ghend- "to seize, to take." The meaning "act of preying or seizing upon anything" is from early 14c.; bird of prey is from late 14c. (fowl of prey is mid-14c.

So from what I understand something to be "prey" it would be something that is seized upon, grasped, or acted upon.  That would makes sense with the example of "birds of prey". Those are birds with talons that grasp their food.  Now I am trying to imagine birds that are flying around "praying" and hoping to find food. I guess that doesn't make sense. They wouldn't be very good predators if they have to rely upon prayer to find their food. What a pathetic plight those birds would be in.