Do you have a C compiler you can use for this? If not, go get one: Google for "open Source C Compiler" or write your own - lots of work.
Then save your program as a specific file, and use Process.Start to run the compiler, giving the file as the input on the command line, and catching the standard output:
Process p = new Process();
p.StartInfo.UseShellExecute = false;
p.StartInfo.RedirectStandardOutput = true;
p.StartInfo.FileName = "MyCCompiler.exe";
p.Arguments = myFileName + " " + myCompilerArguments;
p.Start();
string results = p.StandardOutput.ReadToEnd();
p.WaitForExit();