  We study the nonminimally coupled complex scalar field within the framework
of teleparallel gravity. Coupling of the field nonminimally to the torsion
scalar destroys the Lorentz invariance of the theory in the sense that the
resulting equations of motion depend on the choice of a tetrad. For the assumed
static spherically symmetric spacetime, we find a tetrad which leads to a
self-consistent set of equations, and we construct the self-gravitating
configurations of the scalar field---boson stars. The resulting configurations
develop anisotropic principal pressures and satisfy the dominant energy
condition. An interesting property of the configurations obtained with
sufficiently large field-to-torsion coupling constant is the outwardly
increasing energy density, followed by an abrupt drop towards the usual
asymptotic tail. This feature is not present in the boson stars with the field
minimally or nonminimally coupled to the curvature scalar, and therefore
appears to be a torsion--only effect.
