One of the most elusive features of gamma-ray bursts (GRBs) is the sporadic emission prior to the main prompt event observed in at least ~15% of cases. These precursors have spectral and temporal properties similar to the main prompt emission, and smaller, but comparable, energetics. They are separated from the main event by a quiescent time that may be extremely long, and, in some cases, more than one precursor has been observed in the same burst. Precursors are still a puzzle: despite many attempts, none of the proposed models can account for all the observed features. Based on the complete sample of bright long GRBs observed by Swift (BAT6), we propose a new scenario for which precursors are explained by assuming that the central GRB engine is a newly born magnetar. In this model the precursor and the prompt emission arise from accretion of matter onto the surface of the magnetar. The accretion process can be halted by the centrifugal drag exerted by the rotating magnetosphere onto the infalling matter, allowing for multiple precursors and very long quiescent times.