backlinks? no. twitter is nofollow and don't give a direct link.traffic ? yes. just post your articles on it (if you have ones) and start following people-they will follow you back
well are you using twitter for making good traffic of website because i am also use few months but as yet did not understand that how to work in twitter while my twitter a/c have two thousand more followers and following..not get any hits from twitter so can you guide me where is my mistake of using twitter..
In twitter, you have to share the valuable information which is Fresh and up-to-date. Twitter is a real time application, which means people use it to find information about what’s happening now, not last week, and if we’re tweeting old information people won’t be interested in following us.
As someone already replied above, twitter can't offer backlinks. But it is able to bring A LOT of traffic. They key is to offer interesting content. Follow people working on your niche, make them follow you back. After that, interesting links/articles can be often retweeted. Good luck!