With Facebook's social plugins, you can create a "Like" button which likes a webpage. This defaults to the URL of the page you put it on. However, if you set the page URL to point to a Facebook group, then users who click on it will "like" the group and join it. Twitter's "Tweet" buttons is to tweet the current page, is there a way to make a button which will let users follow your twitter feed with one click, which you can put on your web site / blog?
You certainly can do this.
Documentation is here: http://dev.twitter.com/anywhere/begin#follow-buttons