There are many Socials Automatic Publishing Tools, but most of them are limited or a freemium business model.
Still there are a good free Automatic Publishing tool, it is FeedBurner the web feed management tool of Google.
This option available at Publicize Menu as shown
- After Logged-in your your Feedburner dashboard at feedburner.google.com, using your Google-Account, Enter your Blog's RSS Feed URL.
- After Finishing First step select your Feed and go to Publicize Menu as shown in image above.
- Enable Twitter Account Authentication process by Clicking “Add a Twitter account” button.
- Adjustment your Twitter Automatic Publishing Options.
But What about publishing to my Facebook, Profile or Fan Page!!?
yes, Here's come the trick,
you can enable Twitter Facebook connection, an easy step available into your Twitter Account Seetings and Privacy Menu, That's allow publishing All Tweets, and Tweets cards to Facebook Account Page, or Profile.
Follow Steps as shown into below image.
Hope that Help, Thanks.