  We show how Einstein-Cartan gravity can accommodate both global scale and
local scale (Weyl) invariance. To this end, we construct a wide class of models
with nonpropagaing torsion and a nonminimally coupled scalar field. In
phenomenological applications the scalar field is associated with the Higgs
boson. For global scale invariance, an additional field -- dilaton -- is needed
to make the theory phenomenologically viable. In the case of the Weyl symmetry,
the dilaton is spurious and the theory reduces to a sub-class of one-field
models. In both scenarios of scale invariance, we derive an equivalent metric
theory and discuss possible implications for phenomenology.
