  The interaction of bottom squark-mediated top quark pair production,
occurring in the R-parity violating minimal supersymmetric standard model
(MSSM), is proposed as an explanation of the anomalously large $t\bar{t}$
forward-backward asymmetry (FBA) observed at the Tevatron. We find that this
model can give a good fit to top quark data, both the inclusive and invariant
mass-dependent asymmetries, while remaining consistent (at the 2-$\sigma$
level) with the total and differential production cross-sections. The scenario
is challenged by strong constraints from atomic parity violation (APV), but we
point out an extra diagram for the effective down quark-Z vertex, involving the
same coupling constant as required for the FBA, which tends to weaken the APV
constraint, and which can nullify it for reasonable values of the top squark
masses and mixing angle. Large contributions to flavor-changing neutral
currents can be avoided if only the third generation of sparticles is light.
