  We formulate mimetic theory in f(T) teleparallel gravity where T is torsion
scalar. It is shown that the construction of the mimetic theory in the
teleparallel gravity requires the vierbeins to be left unchanged and the
confomal transformation performed on the Minkowski metric of the tangent space.
It is further argued that the conformal degree of freedom in this teleparallel
mimetic theory becomes dynamical and mimics the behavior of cold dark matter.
We also show that it is possible to employ the Lagrange multipliers method to
formulate the mimetic theory in an f(T) theory without any auxiliary metric.
The mimetic f(T) theory is examined by the method of dynamical system and it is
found that there are five fixed points representing inflation, radiation,
matter, mimetic dark matter and dark energy dominated eras in the theory if
some conditions are satisfied. We examined the power-law model and its phase
trajectories with these conditions.
