  We consider the motion of spinning particles in the field of a well known
vacuum static axially-symmetric spacetime, known as $\gamma$ metric, that can
be interpreted as a generalization of the Schwarzschild manifold to include
prolate or oblate deformations. We derive the equations of motion for spinning
test particles by using the Mathisson-Papapetrou-Dixon equations together with
the Tulczyjew spin-supplementary condition, and restricting the motion to the
equatorial plane. We determine the limit imposed by super-luminal velocity for
the spin of the particle located at the innermost stable circular orbits
(ISCO). We show that the particles on ISCO of the prolate $\gamma$ spacetime
are allowed to have nigher spin than the corresponding ones in the the oblate
case. We determine the value of the ISCO radius depending on the signature of
the spin-angular momentum, ${\rm s-L}$ relation, and show that the value of the
ISCO with respect to the non spinning case is bigger for ${\rm sL}<0$ and
smaller for ${\rm sL}>0$. The results may be relevant for determining the
properties of accretion disks and constraining the allowed values of quadrupole
moments of astrophysical black hole candidates.
