  We shall consider the Schr\"odinger operators on $\mathbf{R}^2$ with random
$\delta$ magnetic fields. Under some mild conditions on the positions and the
fluxes of the $\delta$-fields, we prove the spectrum coincides with
$[0,\infty)$ and the integrated density of states (IDS) decays exponentially at
the bottom of the spectrum (Lifshitz tail), by using the Hardy type inequality
by Laptev-Weidl. We also give a lower bound for IDS at the bottom of the
spectrum.
