The viscoelastic behavior of a nematic dimer is studied by deuteron (H-2) nuclear magnetic resonance (NMR) spectroscopy using a cone-and-plate rheometer. From the H-2 NMR spectra, monitored as a function of the shear rate, the orientation of the director relative to the magnetic field is obtained. Analysis of this experiment, using an analytical and a numerical solution of the Leslie-Ericksen equations, gives detailed information on the viscoelastic properties of the dimer. In particular, the two Leslie viscosities alpha(2) and alpha(3) and the three-dimensional director distribution are determined. The analysis reveals that alpha(2) and alpha(3) are both positive, that is, the dimer is of the flow-aligning type, and the director is tilted by an angle of about 33degrees from the magnetic field toward the velocity axis.