  We point out that relevant constraints on the anomalous magnetic ($a_\tau$)
and electric ($d_\tau$) moment of the tau lepton can be derived from tau-pair
production measurements performed at the LHC. Our conclusion is based on the
observation that the leading relative deviations from the Standard Model
prediction for $pp \to \tau^+ \tau^-$ due to $a_\tau$ and $d_\tau$ are enhanced
at high energies. Less precise measurements at hadron colliders can therefore
offer the same or better sensitivity to new physics with respect to
high-precision low-energy measurements performed at lepton machines. We derive
bounds on $a_\tau$ and $d_\tau$ using the full LHC Run II data set on tau-pair
production and compare our findings with the current best limits on the tau
anomalous moments.
