  We consider the Einstein-Cartan theory with the tetrad $e_{\mu}^{a}$ and spin
connection $\omega_{\mu ab}$ taken as being independent fields. Diffeomorphism
invariance and local Lorentz invariance result in there being two distinct
gauge transformations in this approach, and consequently two ghost fields arise
when employing the usual Faddeev-Popov quantization procedure. Our choice of
gauge fixing retains the gauge invariances of the background field. We show
that the gauge algebra is closed even in the presence of torsion, and the
resulting BRST invariance can be found for the effective action. We also derive
the Slavnov-Taylor identities, which reflect the BRST symmetries of this
theory.
