In 1.5, i had 4 or 5 of them, but i deleted this save. In 1.6, i managed to get 1. From what i remember, sometimes during your day, the shadow of a big bird is shown flying over, above; then, statue appears at a random point in the farm map area.
While in 1.6 i saw quite a few bird shadows flying during certain parts of the day at various days (although fairly rarely), there was no statue to be found, because i had wild grass grow everywhere and built many constructions, effectively minimizing the free space in the field. I am under the impression that you need some basic empty space, in order for the statue to spawn.
Also, there is a similar but different item, with the exact same name, sold at Night Market event ("owl statue"). Those are visibly different and have no relation whatsoever.
