Despite early attempts to determine the optical activity of periodic systems, no general purpose approach is available. Rerát and Kirtman recently presented an implementation of the electric dipole-magnetic dipole polarizability with PBC, which is one of the tensors necessary to evaluate the OR in solids. Here, we present the first derivation of the full OR tensor at density functional theory with PBC (DFT-PBC) level, including both the electric dipole-magnetic dipole and electric dipole-electric quadrupole contributions. This implementation is based on the approach of Scuseria and coworkers to compute the PBC electric dipole-electric dipole polarizability tensor using an atomic orbital (AO) basis . This work reports numerical tests that confirm the correct physical properties of the OR tensor (i.e., its origin invariance), a preliminary analysis of the dependence of the choice of approximate density functional, basis set, and choice of gauge, and a direct comparison with experimental data for the tartaric acid chiral crystal,