The short answer: It is not recommended.
The long answer: Based on existing research related to dogs and some anecdotal reports, most experts do not recommend feeding grapes to cats. There is an unknown medical compound in the fruit that causes acute kidney failure, making it lethal for some animals. Other types of human food that contains grapes or raisins (which are dried grapes) should also not be fed to your cat. These include grape juice, trail mix, raisin bread, raisin cookies, power bars, and wine.
What to do if your cat accidentally eats grapes: Call your veterinarian immediately. Try to find out how many pieces your cat consumed, and observe her for any changes. The toxin may cause her to vomit, have diarrhea, experience abdominal pain, get anorexia, and go through acute renal failure.
In summary: Though there isn’t enough scientific evidence to support that grapes are poisonous for cats, it’s safer to keep this fruit away from your pet. Instead, choose to give her cat-friendly snacks, which should be packed with protein and fat and meet her nutritional requirements. If you’re really keen on feeding her human food, go through our “Can Cats Eat” list to see which ones are safe for her.