Drones will have extensive use cases across various commercial, government, and military sectors, ranging from delivery of consumer goods to search and rescue operations. To maintain safety and security of people and infrastructure, it becomes critically important to quickly and accurately detect non-cooperating drones. In this paper we formulate a received signal strength (RSS) based detector, leveraging the existing wireless infrastructures that might already be serving other devices. Thus the detector should be able to detect the presence of a drone signal buried in radio frequency (RF) interference and thermal noise, in a mixed line-of-sight (LOS) and non-LOS (NLOS) environment. We develop analytical expressions for the probability of false alarm and the probability of detection of a drone, which quantify the impact of aggregate interference and air-to-ground (A2G) propagation characteristics on the detection performance of individual sensors. We also provide analytical expressions for the average network probability of detection, which captures the impact of sensor density on a network's detection coverage. Finally, we find the critical sensor density that maximizes the average network probability of detection for a given requirement of probability of false alarm.