The optical properties of indium islands on GaAs(001) surfaces have been studied by reflectance anisotropy spectroscopy as a function of metal coverage. A large optical anisotropy is observed, which shows an oscillatory behavior and scales with the island size: mean island sizes determined by scanning electron microscope correspond to the wavelengths where extremes in the optical anisotropy arise. We explain this behavior by surface plasmon resonances of the island structure which induce a huge optical anisotropy related to the anisotropic shape and distribution of the In islands. Model calculations of the reflectance anisotropy spectroscopy signal based on a layer system where the island film is represented by an effective medium consisting of ellipsoidal metal particles in a vacuum matrix reproduce the main oscillation and support our conclusion.