We experimentally investigate the effect of flux penetration into the electrodes of a thin-filmYBa2Cu3O7−&dgr;grain boundary Josephson junction using the field-dependent critical current as a probe. Above a temperature-dependent threshold field for flux trapping we observe that the maximum critical currentIcmaxis reduced, and occurs at an applied fieldHpeakshifted from zero. The critical current also has an increasingly complex field-dependent structure. Despite this complexity, we experimentally find thatIcmaxfollows a simple power lawHpeak−0.30.We present a model that predictsIcmax∝Hpeak−1/3due to fluxons trapped in the electrodes. ©1997 American Institute of Physics.