We show that DNA-linked anisotropic doublets composed of paramagnetic colloidal particles can be endowed with controlled propulsion when floating above a flat plate and subjected to a magnetic field precessing around an axis parallel to the plate. The propulsion mechanism for this artificial swimmer does not involve deformations, and it makes use of the minimal two degrees of freedom needed to propel it at low Reynolds numbers. We combine experimental observations with a theoretical analysis that fully characterizes the propulsion velocity in terms of the strength and frequency of the actuating magnetic field.