In this technical note, we provide a method for the asymptotic stabilization of fractional-order linear systems subject to input saturation. Gronwall-Bellman lemma and sector bounded condition of the saturation function are exploited for stability analysis and stabilization of such systems. Based on the proposed stability condition, we provide a bilinear matrix inequality for stability test and an algorithm for estimation of the stable region. Further, we provide an algorithm for state-feedback controller design that maximizes the estimated stable region.