Multi-robot networks use wireless communication to provide wide-ranging services such as aerial surveillance and unmanned delivery. However, effective coordination between multiple robots requires trust, making them particularly vulnerable to cyber-attacks. Specifically, such networks can be gravely disrupted by the Sybil attack, where even a single malicious robot can spoof a large number of fake clients. This paper proposes a new solution to defend against the Sybil attack, without requiring expensive cryptographic key-distribution. Our core contribution is a novel algorithm implemented on commercial Wi-Fi radios that can "sense" spoofers using the physics of wireless signals. We derive theoretical guarantees on how this algorithm bounds the impact of the Sybil Attack on a broad class of robotic coverage problems. We experimentally validate our claims using a team of AscTec quadrotor servers and iRobot Create ground clients, and demonstrate spoofer detection rates over 96%.