We study the delay induced by gravitational light bending in the arrival times of signals emitted by an anisotropic source in rotation (pulsar). The shift of the direction of the allowed pulsar beam (a vector defined by the null geodesic connecting the pulsar to the observer) with orbital phase induces a delay arising from the movement of the pulsar in its orbit (orbital aberration) and another of gravitational origin (gravitational shift delay). The delay due to the orbital aberration has the same dependence on orbital phase as the purely geometric orbital delay and is therefore unobservable. We derive a pulse-timing model for pulsars in massive binaries with high inclination (i=π/2) and negligible eccentricity, adding to the well-known contributions (orbital, Shapiro and non-observable orbital aberration) an extra delay produced by the gravitational shift of the allowed pulsar beam and by an additional (and measurable) term of aberration which appears when the number of pulses is used to define the coordinate time of emission in the pulse-timing model. From the ratio of the pulsar period P to the orbital length L (in c=1 units), the extra and the Shapiro delays are compared. If P/L>=1, the extra delay is the dominant one. Some high-mass X-ray binaries (e.g. Vela X-1) may be ideal scenarios for measuring the extra delay and testing whether pulsars are indeed rotating beacons. However, for X-ray binaries with long pulsar periods, the arrival times are poorly determined and this effect cannot be observed. For high-mass radio binaries, the uncertainties in the determination of the pulse arrival time are small, but the amplitude of the extra delay is also small. The possible discovery of binary pulsars with short periods and significant values of P/L (or the improvement in the measure of arrival times) should allow the observation of this interesting effect involving gravitation and aberration.