Cognitive Radio (CR) is proposed to improve spectral efficiency while avoiding interference with licensed users. In this paper, we propose a Resource Allocation (RA) algorithm to perform uplink frequency allocation and power allocation among non-cooperative multi-cell with multi-user per cell in CR systems. The maximization of total information rate of multiple users in one cell is considered for Rayleigh channel with pathloss, subject to power constraint on each user. Since the optimization formulation for rate maximization of multiple users in each cell is an integer optimization problem, Multiple Access Channel (MAC) technique is proposed. With the aid of MAC, the original integer optimization problem is transformed into a concave optimization problem, thereby we establish a distributed game model, in which the base station of each cell, trying to maximize the sum-rate of its own users, is a player. The proposed game theoretic algorithm for distributed multi-user power allocation is viewed as an extension of Iterative Water-Filling Algorithm (IWFA), which is applied to distributed single-user power allocation. From the perspective of effectiveness, the proposed game theoretic algorithm based on MAC technique is compared to the traditional algorithm based on Frequency Division Multiplexing Access (FDMA). Final numerical results show that the MAC based RA algorithm can achieve more information rate and better convergence performance than FDMA based RA algorithm.