To maintain ideal performance, star trackers must be able to predict the direction of incident starlight to within a few arcseconds across the entire instrument field of view. Parametric camera models are commonly employed to calculate star vectors from camera images and correct for aberrations in the instrument optics. This conventional approach can be quite effective, but systematic errors can be difficult to eliminate and the proper selection of calibration basis functions is often difficult to determine. This study explores using supervised machine learning approaches such as Radial Basis Function networks (RBFNs) and Support Vector Machines (SVMs) for star tracker calibration as an alternative to conventional aberration formulations. These networks can be formulated either as a correction to a low-order camera model or complete replacement for the whole model. When applied to the instrument calibration of a dozen Sinclair Interplanetary ST-16RT2 sensors the RBFN formulation offers 27% reduction in the calibration residuals and almost 12% reduction in the validation residuals over conventional formulations.