In this paper, we focus on the oriented coloring of a graph G. Oriented coloring is a coloring of the vertices of an oriented graph H such that (1) no two neighbors in H are assigned in the same color, and (2) for every two arcs u→v and x→y, if v and x are assigned the same color then u and y cannot be assigned the same color. The oriented chromatic number of a graph G is the maximum oriented chromatic number over all possible orientations of G. In this paper, we derive a lower bound and an upper bound on the oriented chromatic number of honeycomb rectangular tori. Finally, we conjecture to the oriented chromatic number of honeycomb rectangular tori is 10.