I want to add a forum to my website ?

there are a lot solutions:

What is the best free forum software?

Let's explore some of the best community forum software options in more detail:

1. phpBB. phpBB is flexible free forum software that enables you to create boards where registered users can post messages. ...
2. MyBB. ...
3. Vanilla Forums. ...
4. WordPress. ...
5. Joomla! ...
6. Drupal. ...
7. Simple Machines Forum. ...
8. FluxBB.

In themost of the above THERE ARE FREE THEMES. I prefer Vanilla FREE.

if you use a CMS see the repository of plugins/extensions