There is no shortcode and a we cannot access the PHP, let alone, edit it on WordPress.com free hosted blogs: These are the methods you can use:
You can set up Publicize and publish to your Facebook profile page > http://en.support.wordpress.com/publicize/
Alternatively you can use Networked Blogs http://www.networkedblogs.com/ or RSS Grafitti http://www.facebook.com/RSS.Graffiti for posting to Facebook walls if you prefer.
Additional information and links:
You can post a Facebook badge in your sidebar. http://en.support.wordpress.com/facebook-badge/
You can also enable sharing buttons on your posts, pages and index pages.
Also note the “like” button.
You can have Facebook like & share buttons on your posts.
If you wish you can also use the generator to create a “grab my button” code for your friends to use, and place it in your sidebar in a text widget. See here > http://onecoolsitebloggingtips.com/2010/04/16/grab-my-button-code-generator-and-tutorials/