We present a new, model independent method for extracting bounds for the anomalous gamma WW couplings from hadron collider experiments. At the partonic level we introduce a set of three observables which are constructed from the unpolarized differential cross section for the process d (u) over bar-->W- gamma by appropriate convolution with a set of simple polynomials depending only on the center-of-mass angle. One of these observables allows for the direct determination of the anomalous coupling usually denoted by Delta kappa, without any simplifying assumptions, and without relying on the presence of a radiation zero. The other two observables impose two sum rules on the remaining three anomalous couplings. The inclusion of the structure functions is discussed in detail for both <p(p)over bar> an pp colliders. We show that, whilst for <p(p)over bar> experiments this can be accomplished straightforwardly, in the pp case one has to resort to somewhat more elaborate techniques, such as the binning of events according to their longitudinal momenta.