The routinely used procedure for evaluating tunnel positions following anterior cruciate ligament (ACL) reconstructions based on standard X-ray images is known to pose difficulties in terms of obtaining accurate measures, especially in providing three-dimensional tunnel positions. This is largely due to the variability in individual knee joint pose relative to X-ray plates. Accurate results were reported using postoperative CT. However, its extensive usage in clinical routine is hampered by its major requirement of having CT scans of individual patients, which is not available for most ACL reconstructions. These difficulties are addressed through the proposed method, which aligns a knee model to X-ray images using our novel single-image 3D-2D registration method and then estimates the 3D tunnel position. In the proposed method, the alignment is achieved by using a novel contour-based 3D-2D registration method wherein image contours are treated as a set of oriented points. However, instead of using some form of orientation weighting function and multiplying it with a distance function, we formulate the 3D-2D registration as a probability density estimation using a mixture of von Mises-Fisher- Gaussian (vMFG) distributions and solve it through an expectation maximization (EM) algorithm. Compared with the ground-truth established from postoperative CT, our registration method in an experiment using a plastic phantom showed accurate results with errors of (-0.43°±1.19°, 0.45°±2.17°, 0.23°±1.05°) and (0.03±0.55, -0.03±0.54, -2.73±1.64) mm. As for the entry point of the ACL tunnel, one of the key measurements, it was obtained with high accuracy of 0.53±0.30 mm distance errors.