Corrections to the eey and qqy vertices, at the one loop level, from intermediate supersymmetric (SUSY) states are calculated. The induced parity-violating interaction between electrons and nucleons is applied to the calculation of the lowest order SUSY contribution to the asymmetry in deep inelastic e + deuteron scattering in both the 'tree-breaking' (TB) and 'renormalisation-group' (RG) supergravity models. The results indicate that, for a wide range of sparticle masses, the SUSY contributions lie well within constraints implied by present measurements.