Twitter has added a user setting that lets you always use HTTPS when reading and writing on Twitter.com. Twitter is adopting the encryption protocol, in steps.
For some time, users have been able to use Twitter via HTTPS by going to https://twitter.com. Twitter have made it easier for users to do this by adding the option to always use HTTPS.
To turn on HTTPS, go to your settings and check the box next to “Always use HTTPS,” which is at the bottom of the page.
“There are also a few instances where turning on HTTPS in your settings does not force HTTPS. For example, when accessing Twitter from your mobile browser, you need to go to https://mobile.twitter.com to use HTTPS for now. We are working on a solution that will share the “Always use HTTPS” setting across twitter.com and mobile.twitter.com, so you don’t have to think about which device you’re using when you want to check Twitter. If you use a third-party application, you should check to see if that app offers HTTPS.”
More info: http://blog.twitter.com/2011/03/making-twitter-more-secure-https.html