Hey Jeff, yes hunting is legal in Turkey if you get a hunting permit.
There is even something called hunting tourism here in turkey! you can also go hunting with tours or individually. as long as you stick to the designated areas for hunting, and don't shoot the animals not included in the permit, you'll be fine.
The hunting season is autumn and winter.
Here is a detailed post on how to go hunting in Turkey.
Good Luck.

Thanks mate!