Facebook revels the subscribe button for web pages to allow Facebook users to follow each others public updates without the need to connect as friends.
Yes you can embed your facebook profile subscribe button in your site. By default it showing facebook’s founder Mark Zuckerberg subscribe button. You can able to change as your username.
Link to get subscribe button: https://developers.facebook.com/docs/reference/plugins/subscribe
As same like facebook like button you can get in three different sizes, Standard, Button count & Box count.