[en] Linearly and radially polarized multi-terawatt and petawatt laser beams, focused to sub-wavelength waist radii, can directly accelerate protons and carbon nuclei, over micron-size distances, to the energies required for hadron cancer therapy. Radially polarized beams have better emittance than their linearly polarized counterparts. We put forward direct laser acceleration of ions as an appealing alternative for utilization in cancer therapy, once the refocusing of ion beams accelerated by linearly polarized lasers is experimentally solved or radially polarized pulses of sufficient power can be produced. Using a table-top laser system to accelerate the ions may results in a cut on the cost and physical space required by the construction of a conventional accelerator. This scheme may also be a better candidate than the ion production and acceleration by a laser-solid-target method