  In this paper, we consider the $\beta$ function at one-loop approximation for
noncommutative scalar QED. The renormalization of the full theory, including
the basic vertices, and the renormalization group equation are fully
established. Next, the complete set of the one-loop diagrams corresponding to
the first-order radiative corrections to the basic functions is considered:
gauge, charged scalar and ghost fields self-energies, and three- and four-point
vertex functions $\left<\phi^\dag \phi A\right>$ and $\left<\phi^\dag \phi A
A\right>$, respectively. We pay special attention to the noncommutative
contributions to the renormalization constants. To conclude, the one-loop
$\beta$ function of noncommutative scalar QED is then computed and comparison
to known results is presented.
