In this work we report on the observation of surface plasmon properties of periodic arrays of gold nanoring trimers fabricated by electron beam lithography. It is shown that the localized surface plasmon resonances of such gold ring trimers occur in the infrared spectral region and are strongly influenced by the nanoring geometry and their relative positions. Based on numerical simulations of the optical extinction spectra and of the electric near-field intensity maps, the resonances are assigned to surface plasmon states arising from the strong intra-trimer electromagnetic interaction. We show that the nanoring trimer configuration allows for generating infrared surface plasmon resonances associated with strongly localized electromagnetic energy, thus providing plasmonic nanoresonators well-suited for sensing and surface enhanced near-infrared Raman spectroscopy.