Facebook recently implemented Author Tags, which makes it easy for Facebook readers to start following you on Facebook after they have read an article of yours that was shared on Facebook.
Facebook authorship example
The tag enables you to connect your byline in a story preview in the News Feed to your Facebook page or profile with “Follow”.
The connection between byline and Page or Profile is created after a person clicks through a web article posted to Facebook. When the reader returns to News Feed after reading the article, the story preview will display a Follow button at the bottom of the News Feed unit for journalists with Facebook Profiles and a Like button for journalists with Facebook Pages. A text link to the author’s profile or Page is displayed as well. People who click on the Follow or Like button will start receiving updates from the author’s Profile or Page.
Read the Facebook post on Author Tags to implement this for your site(s).