  An improved formula for the timing of binary pulsars that accounts for the
relativistic deflection of light in the gravitational field of the pulsar's
companion is presented, and the measurability of this effect together with its
variance estimates are discussed. The deflection of the pulsar's beam
trajectory in the gravitational field of its companion leads to variation in
the pulsar's rotational phase. This variation appears as the narrow sharp
growth of the magnitude of the post-fit pulsar timing residuals in the vicinity
of the moment of the superior conjunction of the pulsar with its companion. In
contrast to the relativistic Shapiro effect the amplitude of the effect of
gravitational deflection of the pulsar radio beam has two peaks with opposite
signs, which become sharper as the inclination $i$ of the pulsar's orbit
approaches 90$^{\circ}$. The effect under consideration influences the
estimation of parameters of the relativistic Shapiro effect in the binary
pulsars with nearly edgewise orbits. Its inclusion in the fitting procedure
provide more careful measurement of sine of the orbital inclination $i$ as well
as the masses of the pulsar $m_p$ and its companion $m_c$. This permits an
improved testing of alternative theories of gravity in the strong field regime.
Moreover, the measurement of this effect permits independent geometric
constraints on the position of the pulsar rotational axis in space. The effect
of the gravitational deflection of light has been numerically investigated for
binary pulsars with nearly edgewise orbits. It is shown that the effect is
observed in general only when $\cos i\leq 0.003.$ This estimate becomes less
restrictive as the pulsar's spin axis approaches the line of the sight.
