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 $p p rightarrow W^* rightarrow ell u$ 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 $2sigma$.
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