I am struggling to keep turkeys out of my garden. They are constantly digging up all my potatoes

I am trying to grow potatoes this year with straw. Apparently the straw is a huge hit with turkeys. Did you know turkeys can fly over a house? I didn't. But they can. So fences don't keep them out.
I went to a local nursery and asked him about the turkey problem. His answer - a BB gun. He said that is what most people resort to. They can't kill them outside of hunting season, but if you set up station, and every time you see one coming into the garden, hit with a few BB's. He said this seems to be the only method that works.
My son has been enlisted in the turkey war