No. This was implied by the click-baity title on some articles, like [this article on Search Engine Journal](https://www.searchenginejournal.com/chatgpt-watermark/475366/) published after this article, but does not exist.
OpenAI is the company behind GTP2, GTP3, GPT3.5 and also ChatGPT.
They have not released any watermarking technology yet, and non specific to ChatGPT.
When OpenAI release their watermarking, it will get a GPT3 Watermark, a ChatGPT Watermark, a GPT4 Watermark, and so on.