Polls were introduced in October 2015. There is still no public API to create them, view them, or vote in them -- for users using third-party clients, polls are simply invisible.
That's frustrating, I realise. It's probably the most common feature I'm asked about regularly (alongside group Direct Messages). Polls are complicated to add, as there are three aspects (creating, voting, and then seeing the results), and they depend on cards, which are also not currently part of the API. It would be good if we at least added the information that a poll is attached to a Tweet to the Tweet JSON object, even if we can't do all the other things right away. I'd suggest keeping an eye on the roadmap for where we're going, but can't promise those things right now.