  The frequency shift of light in the gravitational field generated by a
rotating body is investigated. We consider the scenario in which both the light
source and the observer are in motion. The frequency shift is calculated up to
the second-order post-Minkowskian approximation via two different methods and
the same result is achieved. The higher-order effects of the gravitational
source's rotation on the frequency shift is obtained. Especially, when both the
light source and the observer are located in the asymptotically flat region, an
elegant formula is obtained, which can be easily used in the astronomical
observations to determine the rotating gravitational source's mass and angular
momentum.
