  Spherically symmetric configurations of the non-interacting massive complex
scalar field, representing non-rotating boson stars, are considered within the
framework of the modified torsion based $f(T)$ gravity, with $f(T) = T + \alpha
\, T^2/2$. We find that with sufficiently large negative value of $\alpha$ the
mass of the boson stars can be made arbitrarily large. This is in contrast to
General Relativity where an upper bound, $M_{max} \sim M_{Planck}^2/m$, to the
mass of the boson stars built from the non-interacting scalar field exists and
where the masses of boson stars in the astrophysical regime can be obtained
only with the introduction of the scalar field self-interaction. With
sufficiently large negative $\alpha$ we also find negative gravitational
binding energy for all masses, which can be seen as an indication of the
stability of such configurations. In its positive regime, $\alpha$ can not be
made arbitrarily large as a phase transition in the stress--energy components
of the $f(T)$-fluid develops. This phenomenon has already been reported to
occur in polytropic stars constructed within the $f(T)$ gravity theory.
