Most of the risk from radon in water comes from breathing the radon it releases, not from drinking it: the lung cancer risk from breathing radon is much larger than the stomach cancer risk from swallowing it. Studies have not confirmed a link between drinking radon in water and stomach cancer.
The source of the water matters. Radon in water is more likely in private wells and in public supplies that use groundwater, and is not usually a problem when the source is surface water, which is where most public supplies come from. Some public systems treat their water for radon before it is delivered.
If the air level is high and your home is on a private well, test the water as well; water tests use different devices and procedures from air tests. Point-of-entry treatment, by aeration or granular activated carbon filters, removes radon before the water reaches your taps, while a device at a single tap treats only a small share of the water.
What to do next: test the air in the lowest lived-in level, and if you are on a private well and the result is high, ask your state radon office about testing the water.