It's amazing to know that internet cats can get viral and attract a crowd of followers in social media. The most famous Twitter cat is Sockington (@sockington). His profile simply says that he is Jason Scott's cat and that his website is sockington.org. His large scale fame in Twitter is because of being featured in the Recommended Feeds which brought in 500 to 5000 likes per day. He was also featured in MSNBC and in the newspaper The Independent. Currently, it is included in the top 100 for the most famous non-human Twitter profiles.
As of February 4, 2018, the @sockington account (https://twitter.com/sockington) has 1.42 million followers. Each post has a huge amount of engagements (likes and retweets).
Sockington's posts sound like the thoughts of a cat. They are presented sometimes in broken english fashion with some of the words in caps.
Here's an example: