I suppose there is a theoretical, unpractical way since it is a two port network of sorts. You would have to terminate it in a short or open, then do sort of an impedance match between it and a reference antenna. This would mean submersing the two in a dielectric or some other media which you could vary the impedance and tune out the reactance to find the efficiency. You would have to know it's pattern, or else measure it from scattering.
Ideally your reference antenna would be an inverse-isotropic antenna, that is a sphere that radiates from it's inner surface towards the center. Place the DUT inside and fill it with with various media until it matches. Maybe you would not have to fill it with media if the sphere was small and the near fields coupled, then you could just tune a matching network on the reference antenna.