In this paper, we discuss gain-scheduled state feedback synthesis for discrete-time systems whose dynamics are characterized by random polytopes, which correspond to polytopes whose vertices are given by random matrices. We first derive a sort of robust stability condition with a parameter-dependent Lyapunov matrix and an auxiliary variable, as a stochastic counterpart of the conventional result for deterministic systems. Then, by extending this condition, we show a matrix inequality based condition that enables us to design gain-scheduled stabilizing state feedback. The effectiveness of the proposed gain-scheduled synthesis is demonstrated with a numerical example.