The short answer is yes. Technically, your cat would be able to eat eggshells. Calcium carbonate is a common source of calcium supplemented in animal food, and calcium carbonate is what makes up an eggshell. With that knowledge, you can see that your cat can consume eggshells to obtain calcium.
But eggshells are not the best source of calcium! Your cat’s usual diet should already contain all the necessary nutrients without adding the calcium that the eggshells would have provided. If you have been serving homecooked meals to your pet, you should be following the instructions that the veterinarian has given you to ensure that all the needed ingredients are present.
Choosing to put eggshells in your cat’s food could work, but you should ask your vet Salem VA for further advice on how much and how often you should be feeding it to your pet.