Walnuts are high in fat, which can upset a cat's digestive system, causing vomiting, diarrhea, and even pancreatitis.
Additionally, they can be a choking hazard and may cause gut obstruction.
Suggestions
It's best to avoid feeding walnuts to your cat.
Instead, consider safer alternatives like small amounts of plain, cooked chicken, turkey, or white fish.
Note: even if labeled as safe, any food can potentially cause allergies. When introducing a new food, please feed a small amount and observe your cat for any allergic reactions.