We report on a new route to grow epitaxial copper (Cu) ultra-thin films (up to 150 nm thick) at ambient temperature on Si(001) wafers covered with native oxide without any prior chemical etching or plasma cleaning of the substrate. It consists of a single-step deposition process using high power impulse magnetron sputtering (HiPIMS) and substrate biasing. For a direct current (DC) substrate bias voltage of -130 V, Cu/Si heteroepitaxial growth is achieved by HiPIMS following the Cu(001) [100]//Si(001) [110] orientation, while under the same average deposition conditions, but using conventional DC magnetron sputtering, polycrystalline Cu films with [111] preferred orientation are deposited. In addition, the intrinsic stress has been measured in situ during growth by real-time monitoring of the wafer curvature. For this particular HiPIMS case, the stress is slightly compressive (-0.1 GPa), but almost fully relaxes after growth is terminated. As a result of epitaxy, the Cu surface morphology exhibits a regular pattern consisting of square-shaped mounds with a lateral size of typically 150 nm. For all samples, X-ray diffraction pole figures and scanning/transmission electron microscopy reveal the formation of extensive twinning of the Cu {111} planes.