A directed triple system of order \(v\), denoted by \(DTS(v)\), is called \((f,k)\)-rotational if it has an automorphism consisting of \(f\) fixed points and \(k\) cycles each of length \((v-f)/k\). In this paper, we obtain a necessary and sufficient condition for the existence of \((f,k)\)-rotational \(DTS(v)\) for any arbitrary positive integer \(k\).