Today, we’re introducing the ability to download your Twitter archive, so you’ll get all your Tweets (including Retweets) going back to the beginning. Once you have your Twitter archive, you can view your Tweets by month, or search your archive to find Tweets with certain words, phrases, hashtags or @usernames.
There’s supposed to be a “Request your archive” button at the bottom of the Settings page, but I don’t see it in my account. This feature hasn’t been rolled out to all users yet. I’ve been maintaining a local archive of my tweets using TweetNest.