Yes it's possible, all you have to do is make your code act as a basic web server. Listen on a port (it doesn't have to be port 80, if IIS is running on the machine it will probably have to be something other than 80 though) and when a request comes in it will be an http request message.
The easiest way to understand what HTTP requests look like is to use the debug tools in your browser and look at the network tab as you request pages, the format is quite simple. Once your service has received a message, parse the request and do whatever work is required to fulfil the request and return an appropriately formatted response. Again you can work out what the response should look like by looking at responses in the debug tools of your browser.
If you google for something like "c# make basic web server" you'll probably find a lot of the code is out there already.