Ever wonder what sites we tend to visit most frequently on the Internet — you know, the series of tubes — say about our political leanings? Us too.

Now we have some answers thanks to a very cool project from Engage DC, a Republican consulting company with a digital focus.

The chart, a bigger version of which you can see here, is absolutely fascinating. (For more on the methodology, scroll to the bottom of this post.)

If you use Spotify to listen to music, Tumblr to consume content or Buzzfeed to keep up on the latest in social media, you are almost certainly a vote for President Obama.

If you buy things on eBay, play FarmVille or search the web with Bing, you tend to favor former Massachusetts governor Mitt Romney. (Google users tilt slightly toward Obama.)

The closest thing to a swing constituency in terms of web habits? For voters who are more politically engaged, it’s Pandora — the online music streaming site.

For the less politically engaged, the swing constituency is the game Angry Birds. So, that happened.

How did Engage DC do it? Here’s Patrick Ruffini, president of the company, explaining.

Over the past few months, we’ve crunched countless ‘Likes’ from thousands of users of Trendsetter, our first-of-its-kind platform that ties together polling, social influence data, and consumer preferences. We’ve used it to map the politics of the social web, analyzing the political partisanship of the user bases of various social properties. Using predictive modeling of Facebook likes, we tied political preferences and engagement to one’s choice of social media.

Great stuff.