Recent methods for people detection in overhead, fisheye images either use radially-aligned bounding boxes to represent people, assuming people always appear along image radius or require significant pre-/post-processing which radically increases computational complexity. In this work, we develop an end-to-end rotation-aware people detection method, named RAPiD, that detects people using arbitrarily-oriented bounding boxes. Our fully-convolutional neural network directly regresses the angle of each bounding box using a periodic loss function, which accounts for angle periodicities. We have also created a new dataset with spatio-temporal annotations of rotated bounding boxes, for people detection as well as other vision tasks in overhead fisheye videos. We show that our simple, yet effective method outperforms state-of-the-art results on three fisheye-image datasets. Code and dataset are available at http://vip.bu.edu/rapid .