While conceptual definitions provide a foundation for the study of disasters and their impacts, the challenge for researchers and practitioners alike has been to develop objective and rigorous measures of resilience that are generalizable and scalable, taking into account spatiotemporal dynamics in the response and recovery of localized communities. In this paper, we analyze mobility patterns of more than 800,000 anonymized mobile devices in Houston, Texas, representing approximately 35% of the local population, in response to Hurricane Harvey in 2017. Using changes in mobility behavior before, during, and after the disaster, we empirically define community resilience capacity as a function of the magnitude of impact and time-to-recovery. Overall, we find clear socioeconomic and racial disparities in resilience capacity and evacuation patterns. Our work provides new insight into the behavioral response to disasters and provides the basis for data-driven public sector decisions that prioritize the equitable allocation of resources to vulnerable neighborhoods.