  As it is well known, symmetry plays a crucial role in the theoretical
physics. On other hand, the Noether symmetry is a useful procedure to select
models motivated at a fundamental level, and to discover the exact solution to
the given lagrangian. In this work, Noether symmetry in f(T) theory on a
spatially homogeneous and anisotropic Bianchi type I universe is considered. We
discuss the Lagrangian formalism of f(T) theory in anisotropic universe. The
point-like Lagrangian is clearly constructed.The explicit form of f(T) theory
and the corresponding exact solution are found by requirement of Noether
symmetry and Noether charge. A power-law f(T), the same as the FRW universe,
can satisfy the required Noether symmetry in the anisotropic universe with
power- law scale factor. It is regarded that positive expansion is satisfied by
a constrain between parameters.
