While you can include social sharing links in your campaigns, it is not possible to auto-post campaigns to Facebook as soon as they're sent to a list of contacts. This is because Facebook no longer allows apps to automatically post content to your profile.
Use social sharing links
You can still get your content posted on Facebook by including the social links content block in your emails. When you include this block, contacts will be able to click the Facebook icon and share your content with their friends.
Read the Social Links help article.