The estimation of the orientation of an observed vehicle relative to an Autonomous Vehicle (AV) from monocular camera data is an important building block in estimating its 6 DoF pose. Current Deep Learning based solutions for placing a 3D bounding box around this observed vehicle are data hungry and do not generalize well. In this paper, we demonstrate the use of monocular visual odometry for the self-supervised fine-tuning of a model for orientation estimation pre-trained on a reference domain. Specifically, while transitioning from a virtual dataset (vKITTI) to nuScenes, we recover up to 70% of the performance of a fully supervised method. We subsequently demonstrate an optimization-based monocular 3D bounding box detector built on top of the self-supervised vehicle orientation estimator without the requirement of expensive labeled data. This allows 3D vehicle detection algorithms to be self-trained from large amounts of monocular camera data from existing commercial vehicle fleets.