In this work, we propose a single-atom interferometer based on a fully two-dimensional spatial adiabatic passage process using a system of three identical harmonic traps in a triangular geometry. While the transfer of a single atom from the ground state of one trap to the ground state of the most distant one can successfully be achieved in a robust way for a broad range of parameter values, we point out the existence of a specific geometrical configuration of the traps for which a crossing of two energy eigenvalues occurs and the transfer of the atom fails. Instead, the wave function is robustly split into a coherent superposition between two of the traps. We show that this process can be used to construct a single-atom interferometer and discuss its performance in terms of the final population distribution among the asymptotic eigenstates of the individual traps. This interferometric scheme could be used to study space-dependent fields from ultrashort to relatively large distances, or the decay of the coherence of superposition states as a function of the distance. © 2014 American Physical Society.