  We quantize a flat cosmological model in the context of $f(T)$ theory of
modified gravity using the Dirac's quantization approach for Hamiltonian
constraint systems. In this regard, first we obtain the Wheeler-DeWitt equation
as the operator equation of the Hamiltonian constraint and solve it for some
typical cosmological models of $f(T)=T-2\Lambda$, $f(T)= \beta\sqrt{-2T}$ and
$f(T)= \gamma T^2$. Then, in the context of classical-quantum correspondence,
we interpret the obtained wavefunctions of the universe to describe an
accelerating de Sitter universe which is found to be in good agreement with
$f(T)=T-2\Lambda$ model. Finally, we study Bohm--de Broglie interpretation of
the quantum model for $f(T)=T-2\Lambda$ model.
