It's a rare event that happens overnight, like the witch, crop fairy, and strange capsule. The stone owl used to be very rare, but happens more often in 1.5. My beach farm is in year 5 and I have 3 stone owls!
The appearance of a Stone Owl used to be a very rare occurrence on the Farm but after the v1.5 update it's become more common to see, maybe happening once every 3 years or so? Keep it and use it for decorating as there's no other way to get it in the game, you can just pickaxe it up and pop it in your statuary with:
Stone Frog
Stone Cairn
Stone Junimo
Chicken Statue