While extensive, research on policing in America has focused on documented actions such as stops and arrests -- less is known about patrolling and presence. We map the movements of over ten thousand police officers across twenty-one of America's largest cities by combining anonymized smartphone data with station and precinct boundaries. Police spend considerably more time in Black neighborhoods, a disparity which persists after controlling for density, socioeconomics, and crime-driven demand for policing. Our results suggest that roughly half of observed racial disparities in arrests are associated with this exposure disparity, which is lower in cities with more supervisor (but not officer) diversity.