Complementing the research of surface plasmon polariton vortices for Archimedean spiral structures grooved in gold platelets, we here study the analogous positive structure of an Archimedean spiral consisting of bent gold nanorods. We consider spirals of two different sizes, for which we perform numerical calculations with the boundary element method. For a micrometer-sized metallic structure we show that the scattered electric field forms a vortex in the centre of the spiral. When the spiral is illuminated by orbital angular momentum light, the topological charge of the vortex can be controlled. For a nanometer-sized plasmonic Archimedean spiral we find that the response to optical excitation is governed by several resonances. When the nanostructure is excited by orbital angular momentum light, different resonances appear compared to the excitation with plane waves. Our results highlight that the distinct architecture of the Archimedean spiral responds in a unique way to the excitation with orbital angular momentum light.