We report on radio continuum observations of the host galaxy of the short gamma-ray burst 071227 (z=0.381) with the Australia Telescope Compact Array (ATCA). We detect the galaxy in the 5.5 GHz band with an integrated flux density of Fnu = 43 +/- 11 microJy, corresponding to an unobscured star-formation rate (SFR) of about 24 Msun/yr, forty times higher than what was found from optical emission lines. Among the ~30 well-identified and studied host galaxies of short bursts this is the third case where the host is found to undergo an episode of intense star formation. This suggests that a fraction of all short-burst progenitors hosted in star-forming galaxies could be physically related to recent star formation activity, implying a relatively short merger time scale.