In this paper we present an alternate formula for calculating gravitational time delay. We use this formula to reduce geodetic Very Long Baseline Interferometry (VLBI) data, taking into account gravitational effects within the Solar System, and to test general relativity. The alternate formula is obtained by expanding the
conventional formula in a Taylor series. We show that the gravitational delay can be split into two terms: a geometric coordinate term; and a term that is explicitly linked to the light deflection angle. Our formula is compared numerically to the conventional formula and arrival times within 1 ps are found at 1$^\circ$ from the Sun for a full range of baseline lengths. We conclude that the standard reduction of geodetic VLBI data for the effects of general relativity is equivalent to the displacement of the reference radio sources from their original catalogue positions in accordance with the classical light deflection formula across the whole sky.