There are a number of ways to do this..
Freds idea might be one of the easiest. Since it has pre built components for dealing with Oauth (the login format used by Twitter) and does require writting any code.
-If your tweets are public facing, and you can view the data without logging in, you may be able to grab the twitter page text with the Isadora TCP-IP actor and parse the text internally either with Text manipulation actors, or with Javascript. This page may help: http://www.dusxproductions.com...
Other possible options
if you have a webserver, you can write a server side script, and use the built in TCP-IP actors to poll your server side script. you could write a script (python, processing, PHP, or any other really) that runs along side Isadora, and checks (polls) twitter to get any new posts every so often [defined period of time].
Sending any result to Isadora via OSC. (much like Freds options)web tools like IFTTT or Zapier (there are many others) can connect to your social media sites, and prepare the content for you in a number of ways.. (you will need to get the data, again tcp-ip or scripting are your options)
PS: What Graham is getting at is that the method of connecting to and working with twitter data changed sometime back. The authentication became much more secure (Oauth) and many things that were open to the public were made restricted to authenticated users. (the format also change from xml to json). JSON is very easy to use in Isadora.