In facts, you do can auto post your web site on account twitter and facebook. there are many ways that allow you to do that. you can do auto post on your twitter on account by using Auto Twitter Latest Post by via FeedBurner and you also can connect your twitter account with facebook as well. More easy ways to that you also find some website that provide this service free and help your site more traffic from those service as well.
Web Site Provide Services Via auto Twitter and Facebook :
Popular web site that used this services such as Mashable, Smashing Magazine, Nettuts+ …etc. so now you also can enjoy free with this service to improve your site traffic as well.