Is there any site provides free forum?

Yes, I know a site called forumotion which provides free forum, I am using them and they are nice. They provide simple forums with various attractive themes. You can try that site. You can check out my forum from my my-lot profile.

I was just wondering why you want to put link of forums to your blog. I suppose you want to join forums to promote your blog. Anyway, there are lot of free forums that you can be a member and they differ according to categories. For webmasters and bloggers, Digital Point and Sitepoint are among the best. However, you should follow their rules so that your account will not be suspended. Incidentally, I just published a blog post entitled How to promote a Blog for Beginners: Part One and forum posting is included. You can find the link on my profile. Hope that helps.

You've forgot to mention what your site is all about. They are right that there are many free forum sites out there and your selection should match your site. Take as many as you like for maximum exposure.