If you live in the EU, you should be able to obtain your entire Tweet history from Twitter under EU privacy laws.
In the UK these laws are backed by the Data Protection Act. To obtain your data from Twitter, you need to send them an email with a Subject Access Request. Once you have your support ticket, you need to fax them some ID. You will then receive an archive of all the data Twitter have about you, including all of your tweets.
This script/class can be used to parse the resulting file so you can stick the data into something a bit more permanent, a database or document store perhaps.
For more details on how to get your data from Twitter, read this article: https://www.privacyinternational.org/blog/what-does-twitter-know-about-its-users-nologs