<p>As of now, there is no such badge. </p>

<p>See also:</p>

<ul>
<li><p><a href="http://meta.stackexchange.com/questions/47718/display-a-happy-birthday-message-when-a-user-logs-in-on-their-birthday">Display a "Happy Birthday" message when a user logs in on their birthday [closed]</a></p></li>
<li><p><a href="http://meta.stackexchange.com/questions/4963/please-award-reputation-equal-to-a-users-age-on-their-birthday-as-a-gift">Please award reputation equal to a user's age on their birthday as a gift</a></p></li>
</ul>