Remove all dishes and food scraps from the sink, especially dark-colored objects that could cause stains.
Turn on the sink. Spray the bowl of the cast iron sink with warm water. Coat the sink with baking soda while the cast iron is wet.
Scrub the sink with a nonabrasive sponge. If black marks do not disappear, add another layer of baking soda. Rinse the sink with clean water when the marks disappear.
Apply a commercial cast iron cleaner if baking soda does not remove the marks. These cleaners contain chemicals that are safe for cast iron and designed to remove stains.