Check if a function exists in a class before calling call_user_func()

You're looking for method_exists for starters. But what you should check, too is whether or not the method is callable. This is done by the helpfully named is_callable function:

if (method_exists($this->controller, $this->view)
    && is_callable(array($this->controller, $this->view)))
{
    call_user_func(
        array($this->controller, $this->view)
    );
}

But that's just the start of things. Your snippet contains explicit require calls, which suggests you're not using an autoloader.
What's more: all you're doing is check file_exists, not if the class was already loaded. Your code, then, will generate a fatal error if, per chance your snippet gets executed twice with the same values for $this->controller.
Begin fixing this by, in the very least, changing your require to require_once...

You can use the PHP function method_exists():

if (method_exists('ClassName', 'method_name'))
call_user_func(etc...);

or also:

if (method_exists($class_instance, 'method_name'))
call_user_func(etc...);