How can I periodically run a Python script to import data into a Django app?
When you are saying " get that data into the DJango app" what exactly do you mean? 
I am guessing that you are using some sort of database (like mysql). Insert whatever data you have collected from your cronjob into the respective tables that your Django app is accessing. Also insert this cron data into the same tables that your users are accessing. So that way your changes are immediately reflected to the users using the app as they will be accessing the data from the same table.
I have a script which scans an email inbox for specific emails. That part's working well and I'm able to acquire the data I'm interested in. I'd now like to take that data and add it to a Django app which will be used to display the information.
I can run the script on a CRON job to periodically grab new information, but how do I then get that data into the Django app?
The Django server is running on a Linux box under Apache / FastCGI if that makes a difference.
[Edit] - in response to Srikar's question When you are saying " get that data into the Django app" what exactly do you mean?...
The Django app will be responsible for storing the data in a convenient form so that it can then be displayed via a series of views. So the app will include a model with suitable members to store the incoming data. I'm just unsure how you hook into Django to make new instances of those model objects and tell Django to store them.