The electrical transport properties of graphene are greatly influenced by its environment. Owing to its high dielectric constant, strontium titanate (STO) is expected to suppress the long-range charged impurity scattering and consequently to enhance the mobility. However, the absence of such enhancement has caused some controversies regarding the scattering mechanism. In graphene devices transferred from SiO2 to STO using a newly developed technique, we observe a moderate mobility enhancement near the Dirac point, which is the point of charge neutrality achieved by adjusting the Fermi level. While bulk STO is not known as a ferroelectric material, its surface was previously reported to exhibit an outward displacement of oxygen atoms and ferroelectric-like dipole moment. When placed on STO, graphene shows strong and asymmetric hysteresis in resistivity, which is consistent with the dipole picture associated with the oxygen displacement. The hysteretic response of the surface dipole moment diminishes the polarizability, therefore weakens the ability of STO to screen the Coulomb potential of the impurities.