Summary: A Cayley map \(M=CM(G,X,p)\) is \(t\)-balanced if \(p(x)^{-1} = p^{t}(x^{-1})\) for all \(x \in X\). Recently, M. Conder, R. Jajcay and T. Tucker [J. Comb. Theory, Ser. B 97, No. 3, 453–473 (2007; Zbl 1113.05045)] classified the regular anti-balanced Cayley maps for abelian groups and J. H. Kwak, Y. S. Kwon and R. Feng [Eur. J. Comb. 27, No. 3, 382–393 (2006; Zbl 1085.05026)] classified the regular \(t\)-balanced Cayley maps for dihedral groups and dicyclic groups [J. H. Kwak and J. Oh, Eur. J. Comb. 29, No. 5, 1151–1159 (2008; Zbl 1165.05013)]. J. Oh [J. Comb. Theory, Ser. B 99, No. 2, 480–493 (2009; Zbl 1208.05054)] classified the regular \(t\)-balanced Cayley maps for semi-dihedral groups. In this paper, we classify the regular \(t\)-balanced Cayley maps for cyclic groups for any \(t\).