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To improve their electrical conductivity for various applications, semiconducting polymer films are often chemically doped to increase their equilibrium charge carrier density. Recently, a novel doping method involving anion exchange has provided control over the identity of the counterions that reside in such films, leading to increased stability under ambient conditions. In this work, however, we show that by ion-exchanging 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane-doped poly(3-hexylthiophene-2,5-diyl) films with hygroscopic salts like bis(trifluoromethane)sulfonimide lithium or LiPF6, the doped film's electrical conductivity drops significantly when exposed to ambient humidity. The change in electrical conductivity depends directly on the degree of hygroscopicity of the counterion and can be over 50% with relatively modest changes in relative humidity (RH), and up to a factor of four between ambient and completely dry conditions. The film's humidity response is entirely reversible when adsorbed water is removed, potentially allowing the doped semiconducting polymer films to function as humidity sensors. Hall effect measurements show that the cause of the drop in conductivity with increasing RH is due to a decrease in carrier mobility and not due to de-doping. Our results emphasize that it is important to control the sample environment when making electrical measurements on anion-exchange doped semiconducting polymer films.