You can setup a custom protocol in Windows and associate it with your program. You have to do this via the Windows registry. Either manually, with a .reg-file or with some kind of installer program which creates the entry for each end user.
Details about this are already answered here How do I register a custom URL protocol in Windows?
Having that registry entry should affect all browsers and will make them open your program whenever a link is using your custom protocol.
Also note that the full URL will be passed to your program as a command line argument. You have to parse that string manually. I assume you're using C# because you used it as a tag. The .NET framework provides methods for parsing URLs and getting the parameters Get URL parameters from a string in .NET