The profiles and the polarization of Ovi lines (lambda6827, 7088) that have been Raman scattered by the atomic hydrogen that is expected in symbiotic stars are calculated. A simple spherical wind model is adopted for the kinematics of the scattering material from the cool giant. Time-dependent perturbation theory is used to calculate the scattering cross-sections, including the continuum contributions. The scattered line profiles from a monochromatic isotropic UV radiation source are investigated adopting a single-scattering approximation, that is all the Raman-scattered photons are assumed to be scattered only once. For a spherical wind model the largest contribution to the scattered flux is due to receding atoms from the hot star, which results in asymmetric profiles to the red. When the scattering optical depth tau_s<~1, in the blue wing strong polarization is shown perpendicular to the binary axis and around the centre the polarization is negligible. For tau_s>~3 the polarization around the centre increases in the direction parallel to the binary axis and the strong polarization perpendicular to the binary axis persists. The synthetic profiles and polarization behaviours are discussed and observational aspects are briefly mentioned. Spectropolarimetry may provide a powerful diagnostic for the kinematic models of symbiotic stars.