  We propose an approach to formulating string theory in a curved spacetime,
which is based on the connection between the states of the WZW model for the
isometry group of a background spacetime metric and the representations of the
corresponding quantum group. In this approach the string states scattering
amplitudes are defined by certain evaluations of the theta spin networks for
the associated quantum group. We examine the evaluations given by the spin
network invariants defined by the spin foam state sum model associated to the
two-dimensional BF theory for the background isometry group. We show that the
corresponding string amplitudes are well defined if the spacetime manifold is
compact and admits a group metric. We compute the simplest scattering
amplitudes in the case of the SU(2) background isometry group, and we provide
arguments that these are the amplitudes of a topological string theory.
