  We compute the one-loop supersymmetric (SUSY) contributions to the weak
charges of the electron ($Q_W^e$), proton ($Q_W^p$), and cesium nucleus
($Q_W^{\rm Cs}$) in the Minimal Supersymmetric Standard Model (MSSM). Such
contributions can generate several percent corrections to the corresponding
Standard Model values. The magnitudes of the SUSY loop corrections to $Q_W^e$
and $Q_W^p$ are correlated over nearly all of the MSSM parameter space and
result in an increase in the magnitudes of these weak charges. In contrast, the
effects on $Q_W^{\rm Cs}$ are considerably smaller and are equally likely to
increase or decrease its magnitude. Allowing for R-parity violation can lead to
opposite sign relative shifts in $Q_W^e$ and $Q_W^p$, normalized to the
corresponding Standard Model values. A comparison of $Q_W^p$ and $Q_W^e$
measurements could help distinguish between different SUSY scenarios.
