Use Facebook’s API. Just add the URL’s you are interested in to the end of of this URL:

http://api.facebook.com/restserver.php?method=links.getStats&urls=

example:

http://api.facebook.com/restserver.php?method=links.getStats&urls=stackoverflow.com,serverfault.com

I think the fancount is just the “like” count of the URL for the FB page.

Source, with PHP code for parsing the output: Get likes on urls from Facebook

 

or

use following

http://graph.facebook.com/?id=http://facebook.com

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