A kinematic theory of reflection high energy electron diffraction (RHEED) is presented for textured polycrystalline thin films. RHEED patterns are calculated for arbitrary texture situations and for any general crystallographic orientation that may be encountered in thin-film growth. It is shown that the RHEED pattern can be used as a fast and convenient tool for in situ texture characterization. The approach also permits quantitative extraction of angular dispersion parameters which are useful for optimizing thin-film growth conditions.