Quantum information protocols often rely on tomographic techniques to determine the state of the system. A popular method of encoding information is on the different paths a photon may take, e.g., parallel waveguides in integrated optics. However, reconstruction of states encoded onto a large number of paths is often prohibitively resource intensive and requires complicated experimental setups. Addressing this, we present a simple method for determining the state of a photon in a superposition of d paths using a rotating one-dimensional optical Fourier transform. We establish the theory and experimentally demonstrate the technique by measuring a wide variety of six-dimensional density matrices. The average fidelity of these with the expected state is as high as 0.9852±0.0008. This performance is comparable to or exceeds established tomographic methods for other types of systems.