  The complete gauge-invariant set of the one-loop QED corrections to the
parity-nonconserving 6s-7s amplitude in $^{133}$Cs is evaluated to all orders
in $\alpha Z$ using a local version of the Dirac-Hartree-Fock potential. The
calculations are peformed in both length and velocity gauges for the absorbed
photon. The total binding QED correction is found to be -0.27(3)%, which
differs from previous evaluations of this effect. The weak charge of
$^{133}$Cs, derived using two most accurate values of the vector transition
polarizability $\beta$, is $Q_W=-72.57(46)$ for $\beta = 26.957(51) a_{\rm
B}^3$ and $Q_W=-73.09(54)$ for $\beta= 27.15(11)a_{\rm B}^3 $. The first value
deviates by $1.1\sigma$ from the prediction of the Standard Model, while the
second one is in perfect agreement with it.
