The effect of radial throughflow on the instability of circular Couette flow is numerically studied for a viscoelastic fluid obeying the Giesekus model. An exact solution has been obtained for the base flow using the perturbation method with the cross-flow Reynolds number serving as the small parameter. The stability of the base flow to infinitesimally small, normal-mode, axisymmetric perturbations is studied using the linear temporal stability theory. An eigenvalue problem is obtained which is solved numerically using the pseudo-spectral, Chebyshev-based collocation method. The numerical results show that for small cross-flow Reynolds numbers, there exists a critical Weissenberg number at which the flow is at its most stable state. For sufficiently large cross-flow Reynolds numbers, however, it is predicted that the flow becomes monotonically less stable when the Weissenberg number is increased. These results suggest that elasticity can be used as an efficient means for the deliberate rise of Taylor cells in rotating micro-filter separators for self-cleaning purposes of the clogged pores.