I've pretty much stated the entire question in the title:
I'm looking for an iPhone application that can call an online API (preferably RESTful but I'll accept anything) as a reaction to triggering a geofence.
So, as a stupid example, a tweet could be sent out automatically when I arrive at my house. The iPhone would see the geofence trigger, the application would be invoked, which would call the Twitter API to send the tweet.