This paper studies the mean-square stabilizability for linear system with random integer-steps delays in discrete time. The fundamental condition of mean-square stabilizability which ensures that an open-loop unstable system can be stabilized by output feedback in the mean-square sense is obtained in terms of applying the Youla parametrization and inner-outer factorization methods to the innovative mean-square small gain theorem. This condition, both necessary and sufficient, provides a fundamental limit imposed by the plant's characteristic (unstable poles, nonminimum phase zeros, relative degree) and the channel's feature (frequency signal-to-noise ratio). The values of the frequency signal-to-noise ratio function at the unstable poles may aggravate the stabilizability condition. Some examples are used to quantify the effect of nonminimum-phase zeros and relative degree of the plant on stabilizability and confirm the correctness of the stabilizability condition.