Save money? You realize the electricity in your car isn't free right? It runs off the alternator which is belt driven by the engine which is powered by gasoline which is more expensive than electricity. The bigger the electric load on the alternator, the more parasitic drag there is. Either way, the power requirments are too small to notice, but you aren't doing yourself any favors in the money saving department.
Yes gasoline is more expensive than electricity, hence a portion of the beauty of electric cars, but I monitor the mileage very very closely in my car and plugging a car charger in has made no discernible difference. The running engine creates enough power/electricity that it can charge a phone and not use extra fuel. And since I've purchased my car about 20% of the miles I've driven are on electric alone. It's definitely saving money as the amount of electricity and fuel needed to run a car so completely dwarfs a car charger it basically has no effect.