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To obtain the receive diversity of timing acquisition, the cooperative processing of multiple distributed received antennas is considered in this paper. In the flat Rayleigh channels, we assume two remote antennas at the base station for receiving the signal transmitted from the mobile station with a single antenna. By utilizing the coverage range of each remote antenna, a constraint is exploited to associate the time-delays from the mobile station to the two remote antennas. With this constraint, we propose a maximum likelihood-based cooperative timing acquisition method to improve the probability of correct acquisition for each remote antenna. Also, a lower bound of the probability of correct acquisition is derived to evaluate the performance of the proposed method. Compared to the independent timing acquisition, the analysis and simulations show that the probability of correct acquisition for each remote antenna can be improved by the cooperation of the two remote antennas.