We have completely characterized which unitary Cayley graphs are Ramanujan. We remark that every case of Theorem 1 gives rise to infinite families of Ramanujan graphs in this form. As shown by Murty in [Murty (2005)], it is impossible to construct an infinite family of k-regular abelian Cayley graphs which are all Ramanujan for any particular k. However, finding examples of Ramanujan graphs in the way that we have presented here is still of some interest. It is also interesting to remark on some other work that has been done on unitary Cayley graphs. Various properties of the graph Xn were determined in [Klotz, W. and Sander, T. (2007)], including the chromatic number, the clique number, the independence number, the diameter, and the vertex connectivity, in addition to some work on the eigenvalues. The energy of Xn was determined and studied independently in [Ili´c (2009)] and [Ramaswamy, H.N. and Veena, C.R. (2009)]. It is also interesting to note that [Ramaswamy, H.N. and Veena, C.R. (2009)] hints at a new approach to finding the eigenvalues of Xn using properties of the graph instead of relying on their expression as Ramanujan sums.