We study the angular fluorescence intensity modulation of a single dye positioned near a spherical gold nanoparticle, induced by rotation of linearly polarized excitation light. Accurate positioning and alignment of nanoparticle and fluorophore with respect to each other and the incoming electric field is achieved by a three-dimensional, self-assembled DNA origami. An intensity map is obtained for a fixed distance and two different nanoparticle diameters, revealing polarization-dependent enhancement and quenching of fluorescence intensity in good agreement to numerical simulations.