  The classical Grunwald--Wang theorem is an example of a local--global (or
Hasse) principle stating that except in some special cases which are precisely
determined, an element $m$ in a number field $\mathbb{K}$ is an $a$-th power in
$\mathbb{K}$ if and only if it is an $a$-th power in the completion
$\mathbb{K}_{v}$ for all but finitely many primes $v$ of $\mathbb{K}$. In this
paper, we prove a Carlitz module analogue of the Grunwald--Wang theorem.
