  We provide a first calculation of the complete next-to-leading order QCD
corrections for heavy flavor contributions to the inclusive structure function
$g_1$ in longitudinally polarized deep-inelastic scattering. The results are
derived with largely analytical methods and retain the full dependence on the
heavy quark's mass. We discuss all relevant technical details of the
calculation and present numerical results for the heavy quark scaling
functions. We perform important crosschecks to verify our results in the known
limit of photoproduction and for the unpolarized electroproduction of heavy
quarks. We also compare our calculations to the available, partial results in
the polarized case, in particular, in the limit of asymptotically large photon
virtualities, and analyze the behavior of the scaling functions near threshold.
First steps towards phenomenological applications are taken by providing some
estimates for inclusive charm production in polarized deep-inelastic scattering
at a future electron-ion collider and studying their sensitivity to the
polarized gluon distribution. The residual dependence of heavy quark
electroproduction on unphysical factorization and renormalization scales and on
the heavy quark mass is investigated.
