Photosynthetic light-harvesting proceeds by the collection and highly efficient transfer of energy through a network of pigment-protein complexes. Inter-chromophore electronic couplings and interactions between pigments and the surrounding protein determine energy levels of excitonic states and dictate the mechanism of energy flow. The excitonic structure (orientation of excitonic transition dipoles) of pigment-protein complexes is generally deduced indirectly from x-ray crystallography in combination with predictions of transition energies and couplings in the chromophore site basis. Here, we demonstrate that coarse-grained excitonic structural information in the form of projection angles between transition dipole moments can be obtained from polarization-dependent two-dimensional electronic spectroscopy of an isotropic sample, particularly when the nonrephasing or free polarization decay signal rather than the photon echo signal is considered. The method provides an experimental link between atomic and electronic structure and accesses dynamical information with femtosecond time resolution. In an investigation of the Fenna-Matthews-Olson complex from green sulfur bacteria, energy transfer connecting two particular exciton states in the protein is isolated as being the primary contributor to a cross peak in the nonrephasing 2D spectrum at 400 fs under a specific sequence of polarized excitation pulses. The results suggest the possibility of designing experiments using combinations of tailored polarization sequencesto separate and monitor individual relaxation pathways.