  This paper formulates, via the Mathisson - Papapetrou - Dixon equations, the
system of equations for a test particle with spin when it is orbiting a weak
Kerr metric. We shall restrict ourselves to the case of circular orbits with
the purpose of comparing our results with the results of the literature. In
particular, we solve the set of equations of motion for the case of circular
trajectories both spinless and spinning test particles around rotating bodies
in equatorial plane. The results obtained are an important guideline for the
study of the effects of the particles with spin in rotating gravitational
fields such as Gravitomagnetics Effects or gravitational waves.
