It is not likely that you would be able to buy hunting items with your food stamp benefits. According to the USDA website:

You can buy any food for the household, such as:

Fruits and vegetables;
Meat, poultry, and fish;
Dairy products;
Breads and cereals;
Other foods such as snack foods and non-alcoholic beverages; and
Seeds and plants, which produce food for the household to eat.

Households CANNOT use SNAP benefits to buy:

Beer, wine, liquor, cigarettes, or tobacco
Vitamins, medicines, and supplements. If an item has a Supplement Facts label, it is considered a supplement and is not eligible for SNAP purchase.
Live animals (except shellfish, fish removed from water, and animals slaughtered prior to pick-up from the store).
Prepared Foods fit for immediate consumption
Hot foods
Any nonfood items such as:
Pet foods
Cleaning supplies, paper products, and other household supplies.
Hygiene items, cosmetics
Retailer Eligibility Resources
https://www.fns.usda.gov/snap/eligible-food-items