We demonstrate a novel position-resolved resonance trimming strategy for silicon ring resonators. Ring resonators are covered with a chromophore-doped guest host polymer cladding. Illumination of the polymer cladding with high-energy electrons causes a bleaching of the chromophore molecules. Bleaching of the chromophores induces a reduction of the polymer refractive index, which can be used to trim the resonance frequency of the ring resonators. A maximum refractive index change of 0.06 and a TM polarization resonance shift of 16.4 nm have been measured. A Q factor of 20,000 before bleaching remains unaltered after the electron beam exposure process.