We examine the influence of the quadrupole moment of slowly rotating neutron stars on the oscillations of non-slender accretion tori. We assume a perfect fluid, polytropic, constant speciﬁc angular momentum, non-selfgravitating torus and analytically calculate formulas for the oscillation frequencies. So far, these have only been studied in the Kerr geometry. We apply known methods for examining the properties of radial and vertical axisymmetric and non-axisymmetric (m = -1) epicyclic modes of oscillating accretion tori in the Hartle-Thorne geometry. Our results are valid within the accuracy of up to second order in the angular momentum of the neutron star and the first order in its quadrupole moment. These can be used to study the properties of relativistic compact objects through the low-mass X-ray binaries phenomenon commonly known as the twin-peak quasi-periodic oscillations.