Is there a way to add static function to Object in AS3

No, that is not possible. Static methods are part of a class definition and need to exist at compile-time. If you need to add functions at runtime that are statically callable, you can do so easily enough with an approach like this:

public class StaticMethods
{
    private static var _map:Object = {};

    public static function add(name:String, method:Function):void
    {
        _map[name] = method;
    }

    public static function call(name:String, ...args):*
    {
        if(_map[name])
        {
            return _map[name].apply(StaticMethods, args);
        }
    }
}

With its usage being like so:

function sum(a:int, b:int):int
{
    return a + b;
}


StaticMethods.add("sum", sum);

trace(StaticMethods.call("sum", 5, 10)); // 15

I wouldn't advise this capability though; it will lead to code that is very difficult to debug and maintain.