  We use the parameterized post-Newtonian (PPN) formalism to explore the weak
field approximation of teleparallel gravity non-minimally coupling to a scalar
field $\phi$, with arbitrary coupling function $\omega(\phi)$ and potential
$V(\phi)$. We find that all the PPN parameters are identical to general
relativity (GR), which makes this class of theories compatible with the Solar
System experiments. This feature also makes the theories quite different from
the scalar-tensor theories, which might be subject to stringent constraints on
the parameter space, or need some screening mechanisms to pass the Solar System
experimental constraints.
