We present a comprehensive temporal and spectral analysis of the long Swift GRB 120327A afterglow data to investigate the possible causes of the observed early time colour variations. We collected data from various instruments/telescopes in different bands (X-rays, ultra- violet, optical and near-infrared) and determined the shapes of the afterglow early-time light curves. We studied the overall temporal behaviour and the spectral energy distributions from early to late times. The ultra-violet, optical, and near-infrared light curves can be modelled with a single power-law component between 200 and 2e4 s after the burst event. The X-ray light curve shows a canonical steep-shallow-steep behaviour, typical of long gamma-ray bursts. At early times a colour variation is observed in the ultra-violet/optical bands, while at very late times a hint of a re-brightening is visible. The observed early time colour change can be explained as a variation in the intrinsic optical spectral index, rather than an evolution of the optical extinction.