  As is well known, symmetry plays an important role in the theoretical
physics. In particular, the well-known Noether symmetry is an useful tool to
select models motivated at a fundamental level, and find the exact solution to
the given Lagrangian. In the present work, we try to consider Noether symmetry
in $f(T)$ theory. At first, we briefly discuss the Lagrangian formalism of
$f(T)$ theory. In particular, the point-like Lagrangian is explicitly
constructed. Based on this Lagrangian, the explicit form of $f(T)$ theory and
the corresponding exact solution are found by requiring Noether symmetry. In
the resulting $f(T)=\mu T^n$ theory, the universe experiences a power-law
expansion $a(t)\sim t^{2n/3}$. Furthermore, we consider the physical quantities
corresponding to the exact solution, and find that if $n>3/2$ the expansion of
our universe can be accelerated without invoking dark energy. Also, we test the
exact solution of this $f(T)$ theory with the latest Union2 Type Ia Supernovae
(SNIa) dataset which consists of 557 SNIa, and find that it can be well
consistent with the observational data in fact.
