An arc-coloring of a digraph G is an assignation of colors to its arcs in such a way that all arcs incident to each vertex, as well as all arcs incident from each vertex, have different colors. In an arc-colored d-regular digraph, each color can be associated to a permutation of the vertices of the digraph. In this paper we show the relation between the permutation group generated by these permutations and the groups of those automorphisms of the arccolored digraph which preserve or exchange colors.