  We discuss a class of teleparallel scalar-torsion theories of gravity, which
is parametrized by five free functions of the scalar field. The theories are
formulated covariantly using a flat, but non-vanishing spin connection. We show
how the actions of different theories within this class are related via
conformal transformations of the tetrad and redefinitions of the scalar field,
and derive the corresponding transformation laws for the free function in the
action. From these we construct a number of quantities which are invariant
under these transformations, and use them to write the action and field
equations in different conformal frames. These results generalize a similar
formalism for scalar-tensor theories of gravity, where the invariants have been
used to express observables independently of the conformal frame.
