As of now, there is no such badge. 

See also:

 - [Display a "Happy Birthday" message when a user logs in on their birthday [closed]](http://meta.stackoverflow.com/questions/47718/display-a-happy-birthday-message-when-a-user-logs-in-on-their-birthday)

 - [Please award reputation equal to a user's age on their birthday as a gift](http://meta.stackoverflow.com/questions/4963/please-award-reputation-equal-to-a-users-age-on-their-birthday-as-a-gift)