There are two ways to do this. The easy out-of-the-box way to do this is to use our softphone app which can open a URL upon incoming call. This is documented in our RC for Desktop User Guide (search for "external app"):
If you don't want to use the softphone approach, you can write an app (will need to define it in the Developer Portal first) that listens for incoming calls and opens a URL in the browser. This can be either Browser-Based app, a widget (the RingCentral Salesforce app does this) or a standalone app.