Roepstorff is a German-origin Danish surname. Notable persons include:
Frederik Adolph de Roepstorff (1842–1883), Danish ethnologist and penal colony superintendent Hans Roepstorff (1910–1945), German chess player Jens Erik Roepstorff (born 1960), Danish handball player Kirstine Roepstorff (born 1972), Danish visual artist