  We study exact solutions of nonlinear electrodynamics coupled to
three-dimensional gravity with torsion. We show that in any static and
spherically symmetric configuration, at least one component of the
electromagnetic field has to vanish. In the electric sector of the theory, we
construct an exact solution, characterized by the azimuthal electric field.
When the electromagnetic action is modified by a topological mass term, we find
two types of the self-dual solutions.
