By definition a scientific belief is a belief that could potentially be falsified. This means that it must through observation or physical experimentation be possible for the belief to be disproved. For more on this see here.
A term used to describe something that is not disprovable is pseudoscience.
Technically the law of attraction is pseudoscience.
This is because no matter what results are produced in the world the law of attraction can justify it. For example if someone says the law of attraction does not work, because they tried it and they did not become rich, then someone who believes in the LoA can say that that person failed because of their lack of belief in the LoA. No matter what result happens someone can just say that it occurred because the law of attraction was in action, but not used properly. This means there can never be a situation where the law of attraction can be disproved.
Does this mean the LoA is a belief system that we should not adopt?
Not necessarily.
I personally have not yet figured out if the LoA is a belief system that works for me. I believe we have a very direct influence over the results we produce in life and these are directly linked to what we focus on and think about most in life. However, there are part of the LoA that I am less certain about, such as manifesting results over which I have no physical influence.
Having said that, I do not believe that the LoA should not be adopted as a belief just because it is not scientific. I believe this, because although the LoA cannot be falsified, it could still be a useful model for explaining our reality and producing results.
Ultimately I believe what really matters is the affect a belief system has on your life. If you want to live a life full of joy, success and love then I believe it is more important that you choose beliefs that will help you achieve these goals in the long term, than choose beliefs because they have strong scientific backing.