Irradiation of a sharp tungsten tip by a femtosecond laser and exposed to a strong DC electric field led to reproducible surface modifications. By a combination of field emission microscopy and scanning electron microscopy, we observed asymmetric surface faceting with sub-ten nanometer high steps. The presence of faceted features mainly on the laser-exposed side implies that the surface modification was driven by a laser-induced transient temperature rise on a scale of a couple of picoseconds in the tungsten tip apex. Moreover, we identified the formation of a nano-tip a few nanometers high located at one of the corners of a faceted plateau. The results of simulations emulating the experimental conditions are consistent with the experimental observations. The presented technique would be a new method to fabricate a nano-tip especially for generating coherent electron pulses. The features may also help to explain the origin of enhanced field emission, which leads to vacuum arcs, in high electric field devices such as radio-frequency particle accelerators.