Today's societies are enveloped in an ever-growing telecommunication infrastructure. This infrastructure offers important opportunities for sensing and recording a multitude of human behaviors. Human mobility patterns are a prominent example of such a behavior which has been studied based on cell phone towers, Bluetooth beacons, and WiFi networks as proxies for location. However, while mobility is an important aspect of human behavior, understanding complex social systems requires studying not only the movement of individuals, but also their interactions. Sensing social interactions on a large scale is a technical challenge and many commonly used approaches---including RFID badges or Bluetooth scanning---offer only limited scalability. Here we show that it is possible, in a scalable and robust way, to accurately infer person-to-person physical proximity from the lists of WiFi access points measured by smartphones carried by the two individuals. Based on a longitudinal dataset of approximately 800 participants with ground-truth interactions collected over a year, we show that our model performs better than the current state-of-the-art. Our results demonstrate the value of WiFi signals in social sensing as well as potential threats to privacy that they imply.