The appearance of spin-1 resonances associated with the electroweak symmetry breaking sector is expected in many extensions of the standard model. We analyze the CERN Large Hadron Collider potential to probe the spin of possible new charged and neutral vector resonances through the purely leptonic processes p p → Z ′ → ℓ + ℓ ' − E T , and p p → W ′ → ℓ ' ± ℓ + ℓ − E T , with ℓ , ℓ ′ = e or μ . We perform a model-independent analysis and demonstrate that the spin of the new states can be determined with 99% C.L. in a large fraction of the parameter space where these resonances can be observed with 100     fb − 1 . We show that the best sensitivity to the spin is obtained by directly studying correlations between the final state leptons, without the need of reconstructing the events in their center-of-mass frames.