We carried out high-sensitivity spectro-polarimetric observations of the central star of the Red Rectangle protoplanetary nebula with the aim of constraining the mechanism that gives its biconical shape. The stellar light of the central binary system is linearly polarised since it is scattered on the dust particles of the nebula. Surprisingly, the linear polarisation in the continuum is aligned with one of the spikes of the biconical outflow. Also, the observed Balmer lines, as well as the Ca ii K lines, are polarised. These observational constraints are used to confirm or reject current theoretical models for the shaping mechanism of the Red Rectangle. We propose that the observed polarisation is not very likely to be generated by a uniform biconical stellar wind. Also, the hypothesis of a precessing jet does not completely match observations since it requires a larger aperture jet than for the nebula.