Quantum state tomography (QST) is a technique used to extract the maximum available information on a state in order to reconstruct its phase-space representation. We address the problem of performing QST on qudits. Our d-dimensional resource is the orbital angular momentum (OAM) of photons. The scheme is based on a quantum algorithm able to perform QST on a density matrix by measuring an ancilla qubit. Our proposal can be implemented using linear optics.