There's no medical evidence that says for sure that cream of tartar removes nicotine from your body but it can help some.
But for some people they said that they did stop smoking easier and sooner after mixing some cream of tartar with some orange juice.
I've never smoked in my life and never will smoke but a coworker used to smoke and she was told by someone else to use cream of tarter in some orange juice and she would then stop smoking sooner and have an easier time with it.
She started using cream of tarter in her orange juice and drank it daily and she found that she did stop smoking sooner so the nicotine must have been getting removed from her body as she stopped craving the nicotine when she used cream of tarter.