As we've noted before, while you don't need a Facebook account to signup and use reInsta, it is very easy to share to FaceBook or Twitter from the reInsta app.
Simply click the share icon in the upper right and choose share photo from the menu that appears. This will open the iOS 6 share dialog to share the photo to any of the social networks you have provisioned on your phone, as shown above. You’ll see familiar icons for Mail, Message, Twitter, and Facebook as well as options for Print, Copy, Use As Wallpaper. Tap on any of those buttons to trigger the related action.
This is a built-in feature of iOS 6. In Settings, you'll find listings for Facebook and Twitter. Go there to set up Facebook and Twitter integration with iOS.