You have a number of options, including plug-ins and free or paid apps, which will let you share your blog on your Facebook page. Facebook also comes with a built-in tool, Notes, that lets you do the same thing. If you add the Notes app to your Facebook FanPage and introduce your blog's RSS feed as a new note, you'll find that Facebook will add a tab with your blog's name and will automatically update your wall stream as you add new blog posts.
Open your fan page and click on the plus key (+) to add the Notes tab. Click on the Notes tab and then click Add New Note. Although you'll get a Write a Note form, just click on the Notes icon that's on the top right-hand corner of the form. The next screen you'll get will say Import a Blog, so type in the URL of your RSS feed and click Start Importing at the bottom of the page. A number of your most recent blogs will jump onto your wall page, and as you publish a new blog, it will automatically be added. It sounds easy, but be aware that it may take a few hours (up to six) until the blog posts actually show up.