Interestingly enough, the answer to your question is a secret! 

It's based on expertise in a tag and activity on the site, but that's about as far as we know.

David Fullerton [posted this on MSE][1]:

>The exact criteria probably won't be announced, because we don't want people to game it. It's not a straight "greater than X reputation", but based on expertise in a tag, and your recent activity on the site.

You can also get invited by going to [this page][2] and clicking the "Request an Invitation" button. 


  [1]: http://meta.stackexchange.com/a/81703/276203
  [2]: http://careers.stackoverflow.com/cv/get-one