A scintillator-type fast ion loss detector (FILD) measures the gyroradius and pitch angle distribution of superthermal ions escaping from a magnetically confined fusion plasma at a single location. Described here is a technique for optimizing the angular orientation of such a detector in an axisymmetric tokamak geometry in order to intercept losses over useful and interesting ranges of pitch angle. The method consists of evaluating the detector acceptance as a function of the fast ion constants of motion, i.e., energy, canonical toroidal momentum, and magnetic moment. The detector acceptance can then be plotted in a plane of constant energy and compared with the relevant orbit class boundaries and fast ion source distributions. Knowledge of expected or interesting mechanisms of loss can further guide selection of the detector orientation. The example of a FILD for the National Spherical Torus Experiment-Upgrade (NSTX-U) is considered.