We show how the $W$ boson polarization in the process of associated $W^{\pm}H$ production at the Large Hadron Collider (LHC) can be used to constrain anomalous $WWH$ couplings. We first calculate the spin density matrix for the $W$ to linear order in the anomalous couplings, which are assumed to be small. We then evaluate angular asymmetries in the decay distributions of leptons produced in the decay of the $W$ and show how they can be used to measure the individual elements of the polarization tensor. We estimate the limits that can be placed on the anomalous $WWH$ couplings at a future run of the LHC.

14 pages, Journal Version