  We use recent observations from solar system orbital motions in order to
constrain f(T) gravity. In particular, imposing a quadratic f(T) correction to
the linear-in-T form, which is a good approximation for every realistic case,
we extract the spherical solutions of the theory. Using these spherical
solutions to describe the Sun's gravitational field, we use recently determined
supplementary advances of planetary perihelia, to infer upper bounds on the
allowed f(T) corrections. We find that the maximal allowed divergence of the
gravitational potential in f(T) gravity from that in the teleparallel
equivalent of General Relativity is of the order of 6.2 \times 10^{-10}, in the
applicability region of our analysis. This is much smaller than the
corresponding (significantly small too) divergence that is predicted from
cosmological observations, as expected. Such a tiny allowed divergence from the
linear form should be taken into account in f(T) model building.
