For a given group Gamma with a generating set A, a dipole with \A\ parallel arcs (directed edges) labeled by elements of A gives rise to a voltage graph whose covering graph, denoted by H(Gamma, A) is a bipartite, regular graph, called a bi-Cayley graph. In the case when Gamma is abelian we refer to H(Gamma,A) as the Haar graph of Gamma with respect to the symbol A. In particular for Gamma cyclic the above graph is referred to as a cyclic Haar graph. A basic theory of cyclic Haar graphs is presented.