Recent observations of an increase in energetic particle intensities on the Voyager 1 spacecraft, for several months in late 2002 to early 2003, suggest new phenomena associated with its approach to the termination shock of the solar wind. An important diagnostic used by the experimenters to interpret the event has been the radial anisotropy of the energetic particle distribution. In this Letter we consider the transport of energetic charged particles accelerated at the termination shock, both in the diffusion approximation and by directly integrating test particle trajectories in a turbulent magnetic field. We determine the radial anisotropy in a number of models. In general, we find that the radial anisotropy of the particles is complicated and that it cannot reliably be used to determine the radial velocity of the background plasma. In all cases considered, we find that the average radial anisotropy in the region upstream of the shock is directed toward the shock and is less than or equal to the Compton-Getting anisotropy in the slower wind downstream. We attribute the difference from the Compton-Getting anisotropy to the diffusive anisotropy, which is directed upstream away from the shock and which is part of the acceleration process. We suggest that the small radial anisotropy observed on Voyager 1 at low energies may actually be an indication that Voyager 1 was located upstream of the shock during the entire event. In addition, we find large fluctuating anisotropies along the magnetic field (nearly transverse to the radial direction).