  Timing a pulsar in a close orbit around the supermassive black hole SgrA* at
the center of the Milky Way would open the window for an accurate determination
of the black hole parameters and for new tests of General Relativity and
alternative modified gravity theories. An important relativistic effect which
has to be taken into account in the timing model is the propagation delay of
the pulses in the gravitational field of the black hole. Due to the extreme
mass ratio of the pulsar and the supermassive back hole we use the test
particle limit to derive an exact analytical formula for the propagation delay
in a Kerr spacetime and deduce a relativistic formula for the frame dragging
effect on the arrival time. As an illustration, we treat an edge-on orbit in
which the frame dragging effect is expected to be maximal. We compare our
formula for the propagation time delay with Post-Newtonian approaches, and in
particular with the frame dragging terms derived in previous works by Wex &
Kopeikin and Rafikov & Lai. Our approach correctly identifies the asymmetry of
the frame dragging delay with respect to superior conjunction, avoids
singularities in the time delay, and indicates that in the Post-Newtonian
approach frame dragging effects are generally slightly overestimated.
