There has been always a question how to track twitter traffic and get the perfect visits which was received by twitter. For it, Danny Sullivan has posted nice article along with detail information, it is worth to take a moment to visit URL Shorterners.
I don't know which method would be best for you, but for me Bit.ly works better. It allows me to track that how many people clicked on the link which I tweeted:

That's why Bit.ly is the most reliable tool for tracking twitter traffic than replaces JavaScript-based packages like Google Analytics or may be other (I don't know)
Let me know what is the powerful tool for you for twitter traffic with reasons.:)