We calculate the prediction for the anomalous weak-magnetic form facto
r of the tau lepton at q(2) = M(Z)(2), within the Standard model. With
all particles on-shell, this is an electroweak gauge invariant quanti
ty. Its value is a(tau)(w)(M(Z)(2)) = - (2.10 + 0.61i) x 10(-6). We sh
ow that the transverse and normal components of the single-tau polariz
ation of tau pairs produced at e(+)e(-) unpolarized collisions are sen
sitive to the real and absorptive parts of the anomalous weak-magnetic
dipole moment of the tau. The sensitivity one can achieve at LEP in t
he measurement of this dipole moment is discussed.