  We reveal that Majorana bound states inside the vortex core in an odd-parity
topological superconductivity classified as "pseudo-scalar" type in the gap
function are distinctly spin-polarized by solving the massive Dirac
Bogoliubov-de Gennes (BdG) equation considering the spin-orbit coupling. This
result is universal for "Dirac superconductivity" whose rotational degree of
freedom is characterized by the total angular momentum J = S + L and in marked
contrast to the spin-degeneracy of the core bound states as the consequence of
the conventional BdG equation. The spin-polarized vortex core can be easily
detected by spin-sensitive probes such as the neutron scattering and other
measurements well above the first critical magnetic field H_{c1}.
