  The energy dependence of the electroweak gauge couplings has not been
measured above the weak scale. We propose that percent-level measurements of
the energy dependence of $\alpha_{1,2}$ can be performed now at the LHC and at
future higher energy hadron colliders. These measurements can be used to set
limits on new particles with electroweak quantum numbers without relying on any
assumptions about their decay properties. The shape of the high invariant mass
spectrum of Drell-Yan, $p p \rightarrow Z^*/\gamma^* \rightarrow \ell^+
\ell^-$, constrains $\alpha_{1,2}(Q)$, and the shape of the high transverse
mass distribution of $p p \rightarrow W^* \rightarrow \ell \nu$ constrains
$\alpha_{2}(Q)$. We use existing data to perform the first fits to
$\alpha_{1,2}$ above the weak scale. Percent-level measurements are possible
because of high precision in theoretical predictions and existing experimental
measurements. We show that the LHC already has the reach to improve upon
electroweak precision tests for new particles that dominantly couple through
their electroweak charges. The 14 TeV LHC is sensitive to the predicted
Standard Model (SM) running of $\alpha_2$, and can show that $\alpha_2$
decreases with energy at $2-3 \sigma$ significance. A future 100 TeV
proton-proton collider will have significant reach to measure running weak
couplings, with sensitivity to the SM running of $\alpha_2$ at $4-5 \sigma$ and
sensitivity to winos with masses up to $\sim$ 1.3 TeV at $2\sigma$.
