A novel object detection method is presented that handles freely rotated objects of arbitrary sizes, including tiny objects as small as $2\times 2$ pixels. Such tiny objects appear frequently in remotely sensed images, and present a challenge to recent object detection algorithms. More importantly, current object detection methods have been designed originally to accommodate axis-aligned bounding box detection, and therefore fail to accurately localize oriented boxes that best describe freely rotated objects. In contrast, the proposed CNN-based approach uses potential pixel information at multiple scale levels without the need for any external resources, such as anchor boxes.The method encodes the precise location and orientation of features of the target objects at grid cell locations. Unlike existing methods which regress the bounding box location and dimension,the proposed method learns all the required information by classification, which has the added benefit of enabling oriented bounding box detection without any extra computation. It thus infers the bounding boxes only at inference time by finding the minimum surrounding box for every set of the same predicted class labels. Moreover, a rotation-invariant feature representation is applied to each scale, which imposes a regularization constraint to enforce covering the 360 degree range of in-plane rotation of the training samples to share similar features. Evaluations on the xView and DOTA datasets show that the proposed method uniformly improves performance over existing state-of-the-art methods.