Early access to The Last of Us' demo will be granted to those who purchase God of War: Ascension upon its release on 13th March.
Naughty Dog's community strategist Eric Monacelli noted on the PlayStation Blog that those who buy God of War: Ascension won't get immediate access, but rather will simply get early access once it becomes available at a later date. Evidently you'll be able to hop into the The Last of Us demo from the God of War main menu, once it's available.
When a commenter asked if the demo would be available to everyone else later, Monacelli replied, "We haven't decided on that yet. It's highly possible but this is the way to get the demo the earliest!"
The Last of Us is due on 7th May exclusively on PS3.