The problem of determining the shape of a two-dimensional inhomogeneous orthotropic scatterer from far-field data is considered. In particular, by using integral equation techniques we prove that the support of the scatterer is uniquely determined if the far-field pattern is known for all incident directions. We point out that this uniqueness result may be useful also for practical applications, since in previously treated cases (isotropic inhomogeneous objects in the case of transverse magnetic incident waves and homogeneous orthotropic objects in the case of transverse electric incident waves) the theorems proving uniqueness have been quite straightforwardly extended to formulate a simple method for solving the inverse scattering problem.