The size-dependent magnetic properties of small iron clusters deposited on ultrathin nickel films have been studied with circularly polarized synchrotron radiation. With the use of sum rules, orbital and spin magnetic moments have been extracted from x-ray magnetic circular dichroism spectra. The ratio of orbital to spin magnetic moments varies considerably with cluster size, reflecting the dependence of magnetic properties on cluster size and geometry. These variations can be explained in terms of enhanced orbital moments in small clusters.