Asteroid (3200) Phaethon is a Near-Earth Apollo asteroid with an unusual orbit that brings it closer to the Sun than any other known asteroid. Its last close approach to the Earth was in mid-December 2017 and the next one will be on October 2026. Previous rotationally time-resolved spectroscopy of Phaethon showed that its spectral slope is slightly bluish, in agreement with its B/F taxonomic classification, but at some rotational phases, it changes to slightly reddish. Motivated by this result we performed time-resolved imaging polarimetry of Phaethon during its recent close approach to the Earth. Phaethon has a spin period of 3.604 hours and we found a variation of the linear polarisation with rotation. This seems to be a rare case in which such variation is unambiguously found, also a consequence of its fairly large amplitude. Combining this new information with the brightness and colour variation, as well as previously reported results from Arecibo radar observations, we conclude that there is no variation of the mineralogy across the surface of Phaeton. However, the observed change in the linear polarisation may be related to differences in the thickness of the surface regolith in different areas or local topographic features.