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.