There's an opensource implementation of the .NET framework called Mono, which runs on many other platforms - Windows, Mac OS X, Linux, Android or even iOS and the engine I'm using (Unity) utilizes Mono. It lacks about a version behind to the official .NET framework, but it's perfectly usable for many applications - after all, it's not like the previous version of the .NET framework was useless.
Technically you could also take just the C# language and use it by itself without .NET framework (which is a huge library that you can utilize in your applications), but you would have to write a lot of functionality yourself then by somehow interfacing it with the system and using the language to specify the algorithms. Or you could create your own library if you desired, so technically it's possible, I'm not sure if there are such tools available though.