We present a versatile method for Fourier encoding the spatial distribution of spins detected by magnetic resonance force microscopy. Shuttling a magnetic particle in synchrony with an rf pulse sequence causes spins in a constant-field slice near the particle to precess at a rate proportional to their x or y coordinate. A two-dimensional spin-density map is recovered by a linear Fourier transform of a set of integrated force signals. Performance of the rf sequence is demonstrated experimentally and numerical simulations show that the method can achieve nanoscale resolution. Our approach offers a new route to manipulating spin wave functions down to the atomic scale.