  In the framework of $f(T)$ gravity, we focus on a weak-field and spherically
symmetric solution for the Lagrangian $f(T)=T+\alpha T^{2}$, where $\alpha$ is
a small constant which parameterizes the departure from General Relativity. In
particular, we study the propagation of light and obtain the correction to the
general relativistic bending angle. Moreover, we discuss the impact of this
correction on some gravitational lensing observables, and evaluate the
possibility of constraining the theory parameter $\alpha$ by means of
observations. In particular, on taking into account the astrometric accuracy in
the Solar System, we obtain that $|\alpha| \leq 1.85 \times 10^{5}\,
\mathrm{m^{2}}$; this bound is looser than those deriving from the analysis of
Solar System dynamics, e.g. $|\alpha| \leq 5 \times 10^{-1}\, \mathrm{m^{2}}$,
$|\alpha| \leq 1.8 \times 10^{4}\, \mathrm{m^{2}}$ or $|\alpha| \leq 1.2 \times
10^{2}\, \mathrm{m^{2}}$ . However we suggest that, since the effect only
depends on the impact parameter, better constraints could be obtained by
studying light bending from planetary objects.
