Traps are localized, deep lying energetic states and are generally considered detrimental for organic semiconducting devices. In this work, we investigate their influence on the magnetic field sensitive current in organic devices, an effect often called organic magnetoresistance. Polymer thin films were doped with materials well known to influence trap characteristics in such devices. We analyzed the observed trends in the intrinsic magnetic field effects in terms of a trapped trion model, which incorporates the spin dependent formation of excitations at these trap sites. The results provide strong evidence that the intrinsic traps in the polymer material are indeed at the origin of these magnetic field effects. This shows that traps have beneficial properties and that their control may provide an appealing route for the engineering of efficient organic magnetic field sensors.