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This paper considers robust pole assignment problem for discrete-time linear periodic systems via linear periodic output feedback. To character a measure for the sensitivity of the eigenvalues of the closed-loop system with respect to perturbations in the coefficient matrices, a robustness index for periodic systems is proposed, which can be regarded as a generalization of robustness index of normal LTI systems. Combined with the complete parametric solutions to pole assignment problem via output feedback in our recent result, the robust pole assignment problem is converted into a static nonconvex optimization problem, which is easily solved by Matlab optimization toolbox. A numerical example is employed to illustrate the effectiveness of the proposed approach.