We study discrete R-symmetries, which appear in the 4D low energy effective field theory derived from heterotic orbifold models. We derive the R-symmetries directly from the geometrical symmetries of the orbifolds. In particular, we obtain the corresponding R-charges by requiring that the couplings be invariant under these symmetries. This allows for a more general treatment than the explicit computations of correlation functions made previously by the authors, including models with discrete Wilson lines, and orbifold symmetries beyond plane-by-plane rotational invariance. The R-charges obtained in this manner differ from those derived in earlier explicit computations. We study the anomalies associated with these R-symmetries, and comment on the results.