Which bit do you want to offload to Azure, the reading of the text file or the polling - or something else? Does your application currently have any WCF involved at all?
If it wasn't for the polling aspect I'd suggest using the Cloud Services option and having a little WCF endpoint on there to receive instructions about which
things to poll. However, web worker processes aren't really designed for long running tasks or tasks which need to run indefinitely, because typically they're often recycled or shutdown for other reasons outside of your control (as the developer).
You could get away with an extra-small Windows VM and a small Windows service with a self-hosted WCF endpoint, which can take care of receiving your instructions (e.g. from your file, submitted over the wire) and handling the polling itself. How much you care about recovery when the service restarts (e.g. due to OS patching) is up to you and probably outside of the scope of your assignment.
What you'll end up with, as Haircut has alluded to, is a client-server application where your server component (in Azure) is doing the real work and your client application is just feeding it instructions, having referenced the .svc endpoint hosted by your server application.
I'm a big fan of WCF and do a lot of work with distributed applications, but haven't done a great deal with Azure. Feel free to hit me up with any questions
