  We consider a fractional Schr\"odinger-Poisson system in the whole space
$\mathbb R^{N}$ in presence of a positive potential and depending on a small
positive parameter $\varepsilon.$ We show that, for suitably small
$\varepsilon$ (i.e. in the "semiclassical limit") the number of positive
solutions is estimated below by the Ljusternick-Schnirelmann category of the
set of minima of the potential.
