Controllable and uniform doping of nanowires (NWs) is the ultimate challenge prior to their effective application. Si NWs amorphize and bend toward the impinging ions under ion irradiation as a result of viscous flow. We demonstrate that thermal annealing induces a full recovery of the crystalline phase corresponding to the unbending of the NWs. The competition between Solid Phase Epitaxy and Random Nucleation and Growth at the nanoscale is the key parameter controlling the recovery.