Apparently, Twitter.com has started supporting Do Not Track (DNT) HTTP header which allows users to opt-out of the online behavioral tracking. Although, Twitter has not announced anything regarding this so far, but a tweet from the official account of Firefox claims so.
DNT was originally proposed by Mozilla, and now has been implemented in all major web browsers except Google Chrome. Chrome has announced to bring support for DNT by the end of this year.
(We will update the post once we get confirmation from Twitter).
Update: Twitter has confirmed this through a tweet.