In a word, "no". Read this advice from International Cat Care on why.
Are you a vegetarian and want your cat to be one too? If you want a vegetarian pet that won’t challenge your beliefs, then it would be better to get a rabbit – a cat is a carnivore first and foremost, and looks and behaves as it does for just this reason.
A cat is what is called an obligate carnivore – it has an absolute need for some of the nutrients found in meat and all of its senses of smell and taste are atuned to being a carnivore – it would be unfair and very dangerous to health to even attempt keeping it as a vegetarian. Feeding your cat or kitten
Read the full article on how to care of your cat here