Single-crystal torque magnetometry performed on weakly-coupled polynuclear systems provides access to a complete description of single-site anisotropy tensors. Variable-temperature, variable-field torque magnetometry was used to investigate triiron(III) complex [Fe3La(tea)2(dpm)6] (Fe3La), a lanthanum(III)-centred variant of tetrairon(III) single molecule magnets (Fe4) (H3tea = triethanolamine, Hdpm = dipivaloylmethane). Due to the presence of the diamagnetic lanthanoid, magnetic interactions among iron(III) ions (si = 5/2) are very weak (<0.1 cm(−1)) and the magnetic response of Fe3La is predominantly determined by single-site anisotropies. The local anisotropy tensors were found to have Di > 0 and to be quasi-axial with |Ei/Di| ~ 0.05. Their hard axes form an angle of approximately 70° with the threefold molecular axis, which therefore corresponds to an easy magnetic direction for the molecule. The resulting picture was supported by a High Frequency EPR investigation and by DFT calculations. Our study confirms that the array of peripheral iron(III) centres provides substantially noncollinear anisotropy contributions to the ground state of Fe4 complexes, which are of current interest in molecular magnetism and spintronics.