The process of shear Alfvén wave resonant absorption for plasma heating has been applied to a theta pinch. The m = 1 mode is excited by means of a helical launching structure with a given wavelength, at a number of different frequencies. When the frequency lies in the continuous Alfvén spectrum the kink energy is transferred to the Alfvén wave and then is rapidly thermalized. The heating power is measured by a diamagnetic probe. It is shown that the probe signal can be treated as a thermodynamic variable permitting an exact energy balance to be deduced. The measured resonance curve of the heating power is in agreement with the predicted behaviour. A 50% efficiency is achieved and the coupling between the plasma and the external circuit is strong, in spite of the high compression ratio.