  The order $\alpha_s^2 \alpha$ mixed QCD and weak corrections to top quark
pair production by quark antiquark annihilation are computed, keeping the full
dependence on the $t$ and $\bar t$ spins. We determine the contributions to the
cross section and to single and double top spin asymmetries at the parton
level. These results are necessary ingredients for precise standard model
predictions of top quark observables, in particular of top spin-induced
parity-violating angular correlations and asymmetries at hadron colliders.
