© 2017 American Physical Society. We report a measurement of the power spectrum of cosmic microwave background (CMB) lensing from two seasons of Atacama Cosmology Telescope polarimeter (ACTPol) CMB data. The CMB lensing power spectrum is extracted from both temperature and polarization data using quadratic estimators. We obtain results that are consistent with the expectation from the best-fit Planck ΛCDM model over a range of multipoles L=80-2100, with an amplitude of lensing Alens=1.06±0.15(stat)±0.06(sys) relative to Planck. Our measurement of the CMB lensing power spectrum gives σ8Ωm0.25=0.643±0.054; including baryon acoustic oscillation scale data, we constrain the amplitude of density fluctuations to be σ8=0.831±0.053. We also update constraints on the neutrino mass sum. We verify our lensing measurement with a number of null tests and systematic checks, finding no evidence of significant systematic errors. This measurement relies on a small fraction of the ACTPol data already taken; more precise lensing results can therefore be expected from the full ACTPol data set.