  We investigate the two-dimensional magnetic Schr\"odinger operator
$H_{B,\beta}=(-i\nabla-A)^2 -\beta\delta(\cdot-\Gamma)$, where $\Gamma$ is a
smooth loop and the vector potential $A$ corresponds to a homogeneous magnetic
field $B$ perpendicular to the plane. The asymptotics of negative eigenvalues
of $H_{B,\beta}$ for $\beta\to\infty$ is found. It shows, in particular, that
for large enough positive $\beta$ the system exhibits persistent currents.
