At a high energy $ep$ collider, such as the Large Hadron-Electron Collider (LHeC) which is being planned at CERN, one can access the $WWgamma$ vertex exclusively in charged current events with a radiated photon, with no interference from the $WWZ$ vertex. We find that the azimuthal angle between the jet and the missing momentum in each charged current event is a sensitive probe of anomalous $WWgamma$ couplings, and show that for quite reasonable values of integrated luminosity, the LHeC can extend the discovery reach for these couplings beyond all present experimental bounds.