Transport critical current measurements have been performed on 5degrees [001]-tilt thin film YBa2Cu3O7-delta single grain boundaries with the magnetic field rotated in the plane of the film, phi. The variation of the critical current has been determined as a function of the angle between the magnetic field and the grain boundary plane. In applied fields above 1 T the critical current j(c) is found to be strongly suppressed only when the magnetic field is within an angle phi(k) of the grain boundary. Outside this angular range the behavior of the artificial grain boundary is dominated by the critical current of the grains. We show that the phi dependence of j(c) in the suppressed region is well described by a flux cutting model.