In this paper, we consider a wireless-powered communication network with transmit antenna selection (TAS), where an energy-limited multi-antenna information source, powered by a dedicated power beacon, communicates with a mobile user (MU). The MU is equipped with a single-antenna and its mobility is characterized by the well-known random waypoint mobility model. Differently from previous works which considered only static scenarios, this paper aims to investigate wireless power and information transfer in the scenario with a random mobile user under Nakagami-m fading. To this end, exact analytical expressions for the outage probability, average delay-limited throughput, ergodic capacity, and average delay-tolerant throughput are derived. The analytical results are compared with Monte-Carlo simulations in order to validate the analysis and provide useful insights on the impact of different parameters on the system performance.