The theory of vortex electron beam electron energy loss spectroscopy (EELS), or vortex-EELS for short, is presented. This theory is applied, using Green function calculations within the finite-difference time-domain method, to calculate spatially resolved vortex-EELS maps of a metal split ring resonator (SRR). The vortex-EELS scattering cross section for the SRR structure is within an order of magnitude of conventional EELS typically for metal nanoparticles. This is promising in terms of feasibility for future measurements to map out the local magnetic response of metal nanostructures and to characterize their magnetic plasmon response in applications, including metamaterials.