  This paper is devoted to the study of Noether gauge symmetries of $f(T)$
gravity minimally coupled with a canonical scalar field. We explicitly
determine the unknown functions of the theory $f(T),V(\phi), W(\phi)$. We have
shown that there are two invariants for this model, one of which defines the
Hamiltonian $H$ under time invariance (energy conservation) and the other is
related to scaling invariance. We show that the equation of state parameter in
the present model can cross the cosmological constant boundary. The behavior of
Hubble parameter in our model closely matches to that of $\Lambda$CDM model,
thus our model is an alternative to the later.
