We investigate the relationship between microstructure and dielectric properties of textured SrTiO3 thin films deposited by radio-frequency magnetron sputtering on epitaxial Pt electrodes on sapphire substrates. The microstructures of Pt electrodes and SrTiO3 films are studied by transmission electron microscopy, atomic force microscopy, and X-ray diffraction. SrTrO3 films grown on as-deposited and annealed Pt electrodes, respectively, consist of a mixture of (111)- and (110)-oriented grains. Temperature-dependent dielectric measurements show that differences in texture and microstructure are reflected in the Curie-Weiss behavior of the SrTiO3 films. Phenomenological models that account for the effects of thermal mismatch strain on the dielectric behavior are developed for different film textures. The models predict that at a given temperature, paraelectric (111)-oriented films of SrTiO3 on tensile substrates will have a higher Curie-Weiss temperature and a greater dielectric constant than (110)-oriented films or bulk SrTiO3. The experimental dielectric behavior is compared with the predictions from theory, and different contributions, such as interfacial layers, film stress, and microstructure, to the Curie-Weiss behavior are discussed.