We report the first detection of gravitational lensing due to galaxy clusters using only the polarization of the cosmic microwave background (CMB). The lensing signal is obtained using a new estimator that extracts the lensing dipole signature from stacked images formed by rotating the cluster-centered Stokes $Q/U$ map cutouts along the direction of the locally measured background CMB polarization gradient. Using data from the SPTpol 500 deg$^{2}$ survey at the locations of roughly 18,000 clusters with richness $lambda ge 10$ from the Dark Energy Survey (DES) Year-3 full galaxy cluster catalog, we detect lensing at $4.8sigma$. The mean stacked mass of the selected sample is found to be $(1.43 pm 0.4) times 10^{14} {rm M_{odot}}$ which is in good agreement with optical weak lensing based estimates using DES data and CMB-lensing based estimates using SPTpol temperature data. This measurement is a key first step for cluster cosmology with future low-noise CMB surveys, like CMB-S4, for which CMB polarization will be the primary channel for cluster lensing measurements.