Yes, it can, but it's definitely not a magic bullet, or any major innovation. It's also not by some chemical reaction as some people assume.
Baking soda is a mild abrasive which is ideal in toothpaste because it's compatible with fluoride, it's not too abrasive as to damage teeth, it's cheap to produce and it's safe to use.
How does it whiten the teeth? Simply by rubbing off the tartar and plaque, which is the mechanism by which toothpaste works.
Salts, either sodium chloride, sodium bicarbonate, or a mixture of both, have also been used for tooth cleaning because of their ready availability and low cost. Because of both their relatively low intrinsic hardness and their high solubility, another advantage is low abrasivity.
--The use of sodium bicarbonate in oral hygiene products and practice.
Baking soda, also known as sodium bicarbonate, is composed of a chemical compound that makes it a great mild abrasive. It is this same abrasiveness that effectively removes surface stains from your teeth and make them appear whiter. However, if your goal is to remove deeper, older stains, then baking soda will not be as effective. You will need to see your dentist or use a product that was specifically created for whitening teeth.