We report the measurement and description of an anisotropy between the in-plane and out-of-plane atomic structure in as-deposited amorphous Tb-Fe alloy films. This anisotropy, measured using a conversion-electron extended x-ray absorption fine structure (EXAFS) technique, correlates closely with measured values of the perpendicular magnetic anisotropy energy as a function of both film composition and annealing temperature. Modeling of the EXAFS data using theoretical codes and structural standards suggests that the Tb-Tb and Fe-Fe pair correlations are greater parallel to the film plane and the Tb-Fe pair correlations are greater perpendicular to the film plane. Upon annealing at 300-degrees-C the structural anisotropy is eliminated and the magnetic anisotropy is lowered to a level consistent with magnetoelastic interactions between the film and substrate.