We propose a version of a gravitational theory with the torsion field, induced by the chameleon field. Following Hojman et al. Phys. Rev. D 17, 3141 (1976) the results, obtained in Phys. Rev. D 90, 045040 (2014), are generalised by extending the Einstein gravity to the Einstein-Cartan gravity with the torsion field as a gradient of the chameleon field through a modification of local gauge invariance of minimal coupling in the Weinberg-Salam electroweak model. The contributions of the chameleon (torsion) field to the observables of electromagnetic and weak processes are calculated. Since in our approach the chameleon-photon coupling constant βγ is equal to the chameleonmatter coupling constant β, i.e. βγ = β, the experimental constraints on β,