For an autonomous vehicle, detecting and tracking other vehicles is a critical task. Determining the orientation of a detected vehicle is necessary for assessing whether the vehicle is a potential hazard. If a detected vehicle is moving, the orientation can be inferred from its trajectory, but if the vehicle is stationary, the orientation must be determined directly. In this paper, we focus on vision-based algorithms for determining vehicle orientation of vehicles in images. We train a set of Histogram of Oriented Gradients (HOG) classifiers to recognize different orientations of vehicles detected in imagery. We find that these orientation-specific classifiers perform well, achieving a 88% classification accuracy on a test database of 284 images. We also investigate how combinations of orientation-specific classifiers can be employed to distinguish subsets of orientations, such as driver's side versus passenger's side views. Finally, we compare a vehicle detector formed from orientation-specific classifiers to an orientation-independent classifier and find that, counter-intuitively, the orientation-independent classifier outperforms the set of orientation-specific classifiers.