Overall rotational anisotropy is found to be generic in compact clusters of model dipolar particles. This broken rotational symmetry, or "global" orientational order, is pronounced in zero temperature configurations. It arises from the tendency of dipolar particles to form head-to-tail chains which encircle the cluster, giving rise to a circulating pattern. In many cases, the zero temperature arrangement of dipolar particles is chiral. Expansion of the dipole density field in vector spherical harmonics provides order parameters to quantify broken orientational symmetry, and facilitates analysis of inversion and reflection symmetry. Finite temperature simulations of a 13-particle cluster with Stockmayer (Lennard-Jones+point dipole) interactions indicates that the global orientational order persists to higher temperatures, even above the point of translational melting. The 13-particle Stockmayer cluster remains orientationally ordered up to the onset of frequent evaporation from the cluster. Ramifications of this effect are discussed.