  In this paper, we study the semiclassical limit for the stationary magnetic
nonlinear Schr\"odinger equation \begin{align}\label{eq:initialabstract}\left(
i \hbar \nabla + A(x) \right)^2 u + V(x) u = |u|^{p-2} u, \quad x\in
\mathbb{R}^{3},\end{align}where $p\textgreater{}2$, $A$ is a vector potential
associated to a given magnetic field $B$, i.e $\nabla \times A =B$ and $V$ is a
nonnegative, scalar (electric) potential which can be singular at the origin
and vanish at infinity or outside a compact set.We assume that $A$ and $V$
satisfy a cylindrical symmetry. By a refined penalization argument, we prove
the existence of semiclassical cylindrically symmetric solutions of upper
equation whose moduli concentrate, as $\hbar \to 0$, around a circle. We
emphasize that the concentration is driven by the magnetic and the electric
potentials. Our result thus shows that in the semiclassical limit, the magnetic
field also influences the location of the solutions of
$(\ref{eq:initialabstract})$ if their concentration occurs around a locus, not
a single point.
