Twitter has just opened up a new tool that allows you to see some detailed statistics when it comes to your account and your tweets.
You can find it at https://analytics.twitter.com
This analytics tool was released a few months back but was only limited to advertisers and verified accounts. Twitter has now made it available to anyone and everyone.
From the analytics tool you can see how many impressions your tweets have received and the engagement rate. You can even track how many times a link you tweeted was clicked.
Unfortunately right now you're only limited to data from the last 28 days. Hopefully Twitter will change that and let you choose specific dates.