We report on the spin properties of bright polariton solitons supported by an external pump to compensate losses. We observe robust circularly polarised solitons when a circularly polarised pump is applied, a result attributed to phase synchronisation between nondegenerate TE and TM polarised polariton modes at high momenta. For the case of a linearly polarised pump either s+ or s- circularly polarised bright solitons can be switched on in a controlled way by a s+ or s- writing beam respectively. This feature arises directly from the widely differing interaction strengths between co- and cross-circularly polarised polaritons. In the case of orthogonally linearly polarised pump and writing beams, the soliton emission on average is found to be unpolarised, suggesting strong spatial evolution of the soliton polarisation, a conclusion supported by polarisation correlation measurements. The observed results are in agreement with theory, which predicts stable circularly polarised solitons and unstable linearly polarised solitons resulting in spatial evolution of their polarisation.