  We consider magnetic Schr\"odinger operator $H=(i \nabla +A)^2-\alpha
\delta_\Gamma$ with an attractive singular interaction supported by a piecewise
smooth curve $\Gamma$ being a local deformation of a straight line. The
magnetic field $B$ is supposed to be nonzero and local. We show that the
essential spectrum is $[-\frac14\alpha^2,\infty)$, as for the non-magnetic
operator with a straight $\Gamma$, and demonstrate a sufficient condition for
the discrete spectrum of $H$ to be empty.
