You can let a bird on your shoulder if it steps on and off at your command, and is behaved there. Don't let your bird just run up your arm to your shoulder. And don't let your bird on your shoulder around strangers or things that can be frightening, sometimes they will bite you to warn you of impending danger!
Personally, I don't have an amazon, but I have a grey who is not allowed on my shoulder. I tried it a couple times and she went right for my earrings, so it's off limits now.