The phonon frequencies at the point, the Born effective charges, and the dielectric permittivity tensors of TiO2 rutile are calculated using the variational density-functional perturbation theory. The calculated phonon frequencies agree with experiment within a few percent. We analyze the corresponding theoretical eigenvectors as well as the interaction of the vibration modes with the electric field. The Born effective charges of TiO2 rutile are much larger than the nominal charges of Ti4+ and O2- ions, as well as those of SiO2 stishovite despite the structural similarity. A giant LO-TO splitting is observed for Eu and A2u modes. The O ions in rutile as well as in stishovite are found to have a counterintuitive reversed electronic polarization near the nuclei. The calculated large, anisotropic static dielectric permittivity tensors as well as electronic dielectric permittivity tensors also compare favorably with experiments.