Deposition of 222 Rn daughters onto detector materials pose a risk to ultra-low background experiments. To mitigate this risk, a common approach is to enclose detector components in sealed plastic bags made of films known to be effective barriers against radon. We describe a new method to evaluate radon barriers which is unique in that (a) it gauges not only the intrinsic resistance to radon penetration of a plastic film but also the integrity of bags fabricated from the film and sealed following some protocol, and (b) it employs gamma spectroscopy rather than alpha spectroscopy. We report the results of applying this method to sealed bags fabricated from polypropylene, Nylon, Mylar, metallized Mylar, FEP, and PFA. Evaluation of the fluoropolymers FEP and PFA as radon barriers are the first such measurements.