How to let the variable be stored in a machine register using C#?

You don't.

Even in C++, the register keyword is only a suggestion. The compiler is free to ignore it.
http://stackoverflow.com/questions/3207018/register-keyword-in-c[^]

In C#, you're not compiling to machine code; you're compiling to MSIL. The JIT compiler later compiles the MSIL to machine code, applying various optimizations to make your code run faster on the current hardware. Adding the register hint to a C# variable would be entirely pointless.