Weak gravitational lensing by large-scale structure in the universe causes deflections in the paths of cosmic microwave background (CMB) photons. This effect introduces statistical anisotropy in the observed CMB temperature and polarization fields. The signature of lensing can be used to reconstruct the projected gravitational lensing potential with a quadratic estimator technique; this provides a measure of the integrated mass distribution out to the surface of last scattering, sourced primarily from redshifts between 0.1 and 5. The power spectrum of the lensing potential encodes information about the geometry of the universe and the growth of structure and can be used to place constraints on the sum of neutrino masses and dark energy. High signal-to-noise mass maps from CMB lensing are also powerful for cross-correlating with other tracers of large-scale structure and for delensing the CMB in search for primordial gravitational waves. This thesis describes a high signal-to-noise reconstruction of the CMB gravitational lensing potential and a measurement of its power spectrum using data from 500 \sqdeg of sky observed between 2012 and 2015 with the polarization-sensitive receiver SPTpol, installed on the South Pole Telescope (SPT). We find the ratio of the lensing spectrum to a theoretical $\Lambda$CDM model to be $A_{\rm \mv}=0.94 \pm 0.05 {\rm\, (stat.)} \pm 0.04 {\rm\, (sys.)}$. This measurement represents a $17.1 \sigma$ constraint on the lensing amplitude and a $41 \sigma$ detection of lensing effects.