Agreed. Paste in the keywords, concatenate it, go to your favorite search engine, and you're ready to rock. You could get fancy and probably have the results pull directly into Excel, but if that is possible, it's over my head.

René seems to have answered this pretty well, but help me understand something, Atul. You want to track traffic coming from Twitter to your website via only tweets you have sent out?

If that is the case, use a URL shortener like bit.ly as René recommends or use the URL builder to segment further. Using the URL builder is in my opinion though a lot of work for likely very little return. But, this at least will tell you how much traffic was generated due to your tweet regardless of whether someone clicked on your link on Twitter.com, in a Twitter app, via an RSS feed, or some other method/channel.

If you instead just want to track all traffic driven by Twitter to your website, why not simply segment out the traffic using something like a GA custom segment? It's not perfect, but it works...especially if you do not limit yourself to just Twitter and instead have a "social media" custom segment, a la http://www.seomoz.org/blog/segmenting-social-traffic-in-google-analytics