Studies of underground miners exposed to radon have consistently demonstrated an exposure-related increase in lung cancer risk; based on this evidence, radon is classified as a known human carcinogen
The way radon is addressed in basements is the sealing of foundation cracks than the installment of a venting system.
In water sources which are high in radon it is proposed that aeration by ventilation is followed by a venting process. This would be a solution of pollution is dilution approach.
The answer to your question depends in part on the scale that you are talking about. For home systems carbon (GAC) filtration of aeration. On a large scale, aeration is a widely used technique. But we really need to know the specifics of the question to fully address it.
Air is mainly composed of nitrogen (N2(gas)) and oxygen (O2(g)). N2 is hydrophobic and O2 is hydrophilic. Injecting pure N2 into water would be more efficient than air (i.e., N2 + O2) in removing radon from water.