  In the supersymmetry (SUSY) models, because of the mass difference between
the left- and right-top squarks, the supersymmetric QCD interactions can
generate parity violating effects in the production of $ t \bar t$ pairs. We
show that SUSY QCD radiative corrections to the parity violating asymmetry in
the production rates of the left- and right-handed top quarks via the $q \bar q
\ra t \bar t$ process can reach about 3% at the Fermilab Tevatron with
$\sqrt{s}=2$ TeV. This could be observable with an integrated luminosity larger
than $2 fb^{-1}$. We also show that in these models the SUSY QCD radiative
corrections to the $t \bar t$ production rate are small unless gluinos are very
light, of the order of 1 GeV.
