Twitter has been usable for a while through SSL. You just needed to remember to go to https://www.twitter.com or have a bookmark set correctly. That is still the more secure way of doing it.
For the rest of us, Twitter now has added a “use SSL” setting. In Twitter, select Settings, scroll to the bottom and select “Always Use HTTPS” and save. You will be prompted for your password. Make sure you see a message “your settings have been changed” after you save.
Twitter reports that if you browse to mobile.twitter.com, you will not be redirected to the secure page. Your mileage may vary with third-party apps.