The simplest solution is just to put the CC folder on that server and then add it's path to your $PATH. Another option is to add it as a resource in the project and then set Copy to Output Dir to Always or If Newer and use a relative path to access it. I believe the second option is better because it removes the outside dependency.
Once you have the file there you can start a command line process with the commands like they have in the docs java -jar compiler.jar --js hello.js --js_output_file hello-compiled.js
and it will do what you want. There is of course also a Java dependency. For some basic info on starting process' in C# check out http://msdn.microsoft.com/en-us/library/system.diagnostics.process(v=vs.110).aspx