Analytics in twitter is now available to all users and not just the advertising partners is going to own this. Christopher Penn discovered this, and wrote about it on his blog, and it has since been picked up by several tech news outlets.
You should be able to access Twitter Analytics by going to settings, Twitter Ads, and from the Ads homepage, going to “Analytics”. From there, you can find “Timeline activity”.
In that Twitter will show you a history of your tweets along with engagement metrics for each tweet: number of favorites, number of retweets and number of replies. You can organize the tweet chart by Best, Good, and All.
If you click on followers in the dash board then you can see a separate dashboard which shows you a follower activity over time. It displays most unique interests of your followers in percentage and as well as follower locations including top cities and gender.
While the offering appears to be available to all Twitter users, it should be noted that the data isn’t completely there for everybody.