  We compute the one-loop supersymmetric (SUSY) contributions to the weak
charges of the electron ($Q_W^e$) and proton ($Q_W^p$) using the Minimal
Supersymmetric Standard Model (MSSM). These $q^2=0$ vector couplings of the
$Z^0$-boson to fermions will be determined in two fixed-target,
parity-violating electron scattering experiments. The SUSY loop contributions
to $Q_W^p$ and $Q_W^e$ can be substantial, leading to several percent
corrections to the Standard Model values for these quantities. We show that the
relative signs of the SUSY loop effects on $Q_W^e$ and $Q_W^p$ are correlated
and positive over nearly all of the MSSM parameter space, whereas inclusion of
R-parity nonconserving interactions can lead to opposite sign relative shifts
in the weak charges. Thus, a comparison of $Q_W^p$ and $Q_W^e$ measurements
could help distinguish between different SUSY scenarios.
