  We present a dual representation for the partition function of 2-dimensional
scalar quantum electrodynamics with a topological term ($\theta$-term). In the
dual representation the complex action problem at non-zero $\theta$ is absent,
which is an obstacle for Monte Carlo simulations in the conventional form of
the model. We discuss the technical aspects of the dual representation and show
that a dual Monte Carlo simulation can be implemented. As a first application
we demonstrate how the $2\pi$-periodicity of physical observables is recovered
in a suitable continuum limit.
