  We consider a non-self-gravitating geometrically thick torus described by
Weyssenhoff ideal spin fluid in a black hole spacetime. The Weyssenhof spin
fluid shares the same symmetries of the background geometry, i,e. stationarity
and axisymmetry and further describes circular orbital motion in the black hole
spacetime. We further assume that assume the alignment of the spin is
perpendicular to the equatorial plane. Under this setup, we determine the
integrability conditions of the general relativistic momentum conservation
equation of Weyssenhoff ideal spin fluid using the Frenkel spin supplementary
condition. In the light of the integrability conditions, we then present
stationary equilibrium solutions of the spin fluid torus with constant specific
angular momentum distributions around the Schwarzschild black hole by
numerically solving the general relativistic momentum conservation equation.
Our study reveals that both the iso-pressure and iso-density surfaces of torus
get significantly modified in comparison to the ideal fluid torus without a
spin fluid, owing to the spin tensor and its coupling to the curvature of the
Schwarzschild black hole. In fact, the size of the torus is also found to be
enhanced (diminished) depending on positive (negative) magnitude of spin
parameter $s_0$. We finally estimate the magnitude of $s_0$ by assuming the
torus to be composed of spin-1/2 particles.
