  We examine quantum corrections of time delay arising in the gravitational
field of a spinning oblate source. Low-energy quantum effects occurring in Kerr
geometry are derived within a framework where general relativity is fully seen
as an effective field theory. By employing such a pattern, gravitational
radiative modifications of Kerr metric are derived from the energy-momentum
tensor of the source, which at lowest order in the fields is modelled as a
point mass. Therefore, in order to describe a quantum corrected version of time
delay in the case in which the source body has a finite extension, we introduce
a hybrid scheme where quantum fluctuations affect only the monopole term
occurring in the multipole expansion of the Newtonian potential. The predicted
quantum deviation from the corresponding classical value turns out to be too
small to be detected in the next future, showing that new models should be
examined in order to test low-energy quantum gravity within the solar system.
