  The presence of spinor fields is considered in the framework of some
extensions of teleparallel gravity, where the Weitzenb\"ock connection is
assumed. Some well known models as the Chaplygin gas and its generalizations
are reconstructed in terms of a spinor field in the framework of teleparallel
gravity. In addition, the {\Lambda}CDM model is also realized with the presence
of a spinor field where a simple self-intercating term is considered and the
corresponding action is reconstructed. Other cosmological solutions and the
reconstruction of the gravitational action in terms of the scalar torsion is
studied.
