Convert php permalink to short url?

I have this code that allows users to send a tweet from my blog. It send a tweet for a specific post:

<a href="https://twitter.com/home?status=Currently reading <?php the_permalink(); ?>" title="Click to send this page to Twitter!" target="_blank">Tweet This!</a>

It works great, but I am trying to figure out how to have it convert the permalink to a short url, so the longer urls in my blog will work in Twitter (long urls get cut off). I know there is a wordpress plugin (tweet this) that has this feature, but I can’t use that plugin for various reasons.

Thank you for any suggestions.