Currently, we do not have a built-in output pipe for Facebook which will allow you to post your news items or any content items from Sitefinity to Facebook.
What I can suggest is to use the built-in functionality of the Sitefinity feeds and create RSS feeds
in Sitefinity that are populated for example by the Sitefinity news items content or Sitefinity blog posts. You can then import these feeds in Facebook using third party tools.
We have also logged a feature request to have this functionality out of the box. Here is the link
to the feedback portal where you can vote to increase the popularity of the feature request and track its progress.
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Sitefinity CMS Ideas&Feedback Portal
and vote to affect the priority of the items