I have a pet project that is an online game, the entire game engine is written in C# and I would like to know if there is anyway I can call the functions of this existing as
You might have some luck with this project, which is a port of Node.js to .NET. I haven't used it myself, but with a native .NET implementation you theoretically should be able to do what you need to.
You might also want to go the other direction and try to port (aka: recompile unless you're hooked deep into Windows) your C# game engine to Mono and see if you can then build wrappers off of that.