This is exercise 9 of chapter 0 from Do Carmo's book in Riemannian Geometry:
Let $G\times M \rightarrow M$ a properly discontinuous action from a Group $G$ on a smooth manifold $M$. Prove that $\frac{M}{G}$ is orientable if and only if there is a orientation of $M$ who is preserved by all diffeomorphism of $G$