Can I use a class method as a delegate callback

First, I assume by "static" methods, you mean class methods (declared with + instead of -).

"The compiler does not complain" about Objective-C doesn't always tell you much. All it really means is that you have convinced the compiler that everything should (or at least could) work at runtime.

In the end, if the object you provide as a delegate responds to the right messages, the compiler won't care that it's a class (and neither will the runtime). In this case, you are providing self from a class method. It is as though you typed [MyClass class].

I think it's probably questionable whether this is what you should do--but that's probably outside the bounds of your question.

I would like to share some of my findings:

1. It does not matter whether I declare the delegate like this delegate:self or delegate:[MyClass class]

2. However, it does matter how I declare the method:

   This works

   +(void)alertView:(UIAlertView *)alertView clickedButtonAtIndex:(NSInteger)buttonIndex{
       // Some Actions here
   }
   

   Although the following "syntax" is the declaration in the UIAlertViewDelegate protocol, it does not work:

   // Mind the `-` sign at the start of the line.
   -(void)alertView:(UIAlertView *)alertView clickedButtonAtIndex:(NSInteger)buttonIndex{
       // Some Actions here
   }