Photon emission spectra of individual alumina-supported silver clusters have been measured for the first time. The light emission stimulated by electron injection from the tip of a scanning tunneling microscope can be assigned to the (1,0) mode of the Mie-plasmon resonance in small silver particles. As cluster sizes decrease, the resonance position shifts to higher energies and the linewidth increases. In the size range examined (1.5-12 nm), intrinsic size effects are discussed as possible origins for the observed size dependence of the Mie resonance.