If you want your cat to be on social media and you do not want to register it on Facebook (obviously, but you know it is a lie if I say that there are no animals on Facebook), Catmoji might be the closest you can get.
The people behind Catmoji site are Matthew Phiong and Koekoe Loo Wan Koe from Malayisa. They hoped to achieve something like Facebook but for cats. From the site: -
What is Catmoji?
Catmoji is a place for cat lovers to share and discover cat pictures and videos by expressing themselves through emoji.
Catmoji is on a mission to make the Internet a better and happier place with cats. Join and help us distrupt the Internet with cats and happiness.
Quick, start registering your cat(s) to the network so that all of them can be connected on social media.