We derived an overall piezoresistance tensor for polycrystalline aggregates having an orthotropic texture using the crystallite orientation distribution function (CODF) and the cubic single-crystal piezoresistance tensor. We found that the deviatoric part of the overall piezoresistance tensor has a functional dependence on the preferential crystallographic orientation of cubic single crystals and that the tensor has three independent components. The physical properties of the tensor are invariant under the choice of the CODF. We applied the CODF defined by Roe to calculate the tensor for a fiber texture. Furthermore, we compared the experimental results for the piezoresistance of polysilicon with our theoretical analysis results. The experimental results indicate that the variation in texture strength plays a major role in representing the piezoresistance anisotropy of polycrystalline aggregates.