There's many ways to do this depending on what site your blog is through.
One easy way is to get a free Hootsuite account http://hootsuite.com. On the free account you can have 2 RSS feeds. Just connect your Facebook and/or facebook page and go to Settings > RSS/Atom.
If you are using Wordpress, Tumblr, Or blogspot/blogger then you could use http://IFTTT.com (if this then that). Also free and you just go to the channels tab and link them together. Then browse for an already made "recipe" that says any time I post to wordpress > goes to facebook page.
Then there's also several apps right through Facebook that will do it too.
I just tested the Involver one for you it's http://www.involver.com/applications/ took about half a minute to set up and works great as well.