This is very easy to find out just go to the following address and replace the Highleted part with your Twitter Username.

http://twitter.com/users/show/jtperman.xml

Once on the site search for "created_at" (can search by useing Ctrl+F)
The age of your Twitter account is the first <created_at></created_at> tag
If you see my account it was created Wed June 3rd, 2009 at 12:34:03am