Is it possible to make an ads campaign on Facebook to promote a Facebook group?

You can post detailed write ups about what your page is all about and then add the link to your page in the write up. That way anyone who reads the post can easily click on the link and gets redirected to your page

It is not.
However, you can write a post on your FB page and boost the post with their ad platform.

Read this article for more info:
https://moz.com/blog/how-to-build-a-facebook-group

Cheers!