We study a quasi-two-dimensional monolayer of granular rods fluidized by a spatially and temporally homogeneous upflow of air. By tracking the position and orientation of the particles, we characterize the dynamics of the system with sufficient resolution to observe ballistic motion at the shortest time scales. Particle anisotropy gives rise to dynamical anisotropy and superdiffusive dynamics parallel to the rod’s long axis, causing the parallel and perpendicular mean-square displacements to become diffusive on different time scales. The distributions of free times and free paths between collisions deviate from exponential behavior, underscoring the nonthermal character of the particle motion. The dynamics show evidence of rotationaltranslational coupling similar to that of an anisotropic Brownian particle. We model rotational-translational coupling in the single-particle dynamics with a modified Langevin model using nonthermal noise sources. This suggests a phenomenological approach to thinking about collections of self-propelling particles in terms of enhanced memory effects.