  We study the following singularly perturbed nonlocal Schr\"{o}dinger equation
$$ -\vr^2\Delta u +V(x)u =\vr^{\mu-2}\Big[\frac{1}{|x|^{\mu}}\ast F(u)\Big]f(u)
\quad \mbox{in} \quad \R^2, $$ where $V(x)$ is a continuous real function on
$\R^2$, $F(s)$ is the primitive of $f(s)$, $0<\mu<2$ and $\vr$ is a positive
parameter. Assuming that the nonlinearity $f(s)$ has critical exponential
growth in the sense of Trudinger-Moser, we establish the existence and
concentration of solutions by variational methods.
