"Twitter has started rolling out the option for users to download their Twitter archive. That file will contain all your tweets up until the time you download it, arranged chronologically and searchable."
One caveat: The feature is still being rolled out, so isn't available to all users yet. Check the bottom of your Settings page.
Answer
There is now:
"Twitter has started rolling out the option for users to download their Twitter archive. That file will contain all your tweets up until the time you download it, arranged chronologically and searchable."
One caveat: The feature is still being rolled out, so isn't available to all users yet. Check the bottom of your Settings page.