Yes, baking soda is a great household item to clean the faucets corroded from rust. Make a thick paste with equal parts of water and baking soda, you may also add a few drops of mild dishwashing agent to the paste. Apply the paste to the faucet and leave for a few minutes. Now scrub vigorously with a toothbrush or a scrub brush until you see the rust coming off. Finally, rinse with water and wipe with a soft cloth.