Drone detection has benefited from improvements in deep neural networks, but like many other applications, suffers from the availability of accurate data for training. Synthetic data provides a potential for low-cost data generation and has been shown to improve data availability and quality. However, models trained on synthetic datasets need to prove their ability to perform on real-world data, known as the problem of sim-to-real transferability. Here, we present a drone detection Faster-RCNN model trained on a purely synthetic dataset that transfers to real-world data. We found that it achieves an AP_50 of 97.0% when evaluated on the MAV-Vid - a real dataset of flying drones - compared with 97.8% for an equivalent model trained on real-world data. Our results show that using synthetic data for drone detection has the potential to reduce data collection costs and improve labelling quality. These findings could be a starting point for more elaborate synthetic drone datasets. For example, realistic recreations of specific scenarios could de-risk the dataset generation of safety-critical applications such as the detection of drones at airports. Further, synthetic data may enable reliable drone detection systems, which could benefit other areas, such as unmanned traffic management systems. The code is available https://github.com/mazqtpopx/cranfield-synthetic-drone-detection alongside the datasets https://huggingface.co/datasets/mazqtpopx/cranfield-synthetic-drone-detection.