Yes, you can simply throw an exception in your constructor. If you're simply creating a guard statement to prevent someone from providing bad arguments, then that's fine.
public MyClass(int a, int b, int c)
{
if(c != 1 && c != 2)
throw new ArgumentException(...);
...
}
But if the calling code will want to know whether the arguments are valid before attempting to construct the object, you may be better off using some kind of Builder class to validate your parameters and allow you to programmatically know if there's going to be a problem beforehand.