  We study loop-induced parity violating asymmetries in the strong production
of polarized top quark pairs at $pp$ and $p \bar p$ colliders. The electroweak
${\cal O}(\alpha)$ corrections to the helicity amplitudes of $q \bar q \to t
\bar t$ and $gg \to t \bar t$ are evaluated in a two Higgs doublet model (2HDM)
and the minimal supersymmetric standard model (MSSM). While observables in top
quark pair production receive little contribution from standard electroweak
interactions, it is possible that they can be significantly enhanced in a 2HDM
and the MSSM. We find that the one-loop MSSM electroweak corrections can
generate parity violating asymmetries in the total production rate of left- and
right-handed top quark pairs up to about 1.7% at the upgraded Tevatron
($\sqrt{S}=2$ TeV) and 3% at the LHC ($\sqrt{S}=14$ TeV).
