In this work, we report on the demonstration of an electrically injected AlGaN nanowire laser operating at 239 nm at room temperature. Vertically aligned Al-rich AlGaN nanowires are grown on Si substrate by plasma-assisted molecular beam epitaxy. It is observed that the randomly distributed AlGaN nanowires can strongly confine photons in the deep ultraviolet wavelength range, due to the recurrent multiple scattering of light and the inversely tapered nanowire geometry. The laser exhibits a very low threshold current of 0.35 mA at room temperature. From the detailed rate equation analysis, the spontaneous emission coupling factor is derived to be around 0.012.