I can only hope Tugbrethil will answer - in the UK we do not have wild turkeys - good luck

Don't have wild turkeys here in the low desert, either! A good fence around the garden could help, but that's a little iffy, since truly wild turkeys can fly! At worst, you could do what some of our more rural residents do, and enclose the entire garden in a chicken wire cage--though they are more concerned with starlings and crows than turkeys. A mid-size or larger dog could help, but sometimes dogs do more damage than the turkeys would. I would also double check with your local wildlife management bureau, since wild turkeys are protected in some states. I'll also check with some of my friends in Flagstaff, Arizona, where they do have wild turkeys, but that isn't something that they have complained about before.