Conventional array code acquisition uses a correlator bank and an adaptive beamformer. However, its performance degrades significantly while multiple access interference (MAI) is present. In this paper, we propose a low-complexity adaptive filtering scheme to solve the problem. The proposed scheme comprises two adaptive filters, an adaptive spatial and an adaptive temporal filter. With a special structure, the spatial filter can act as a beamformer suppressing interference, while the temporal filter can act as a code-delay estimator. A criterion is proposed for minimization such that these filters can simultaneously adjusted by a constrained least-mean-square (LMS) algorithm. The proposed system is simple and it can acquire both the code-delay and direction-of-arrival (DoA) of the desired user. The performance as well as the convergence behavior of the proposed algorithm is analyzed. Closed-form expressions for optimum filters and steady-state mean-squared errors (MSE) are derived. Computer simulations show that the mean acquisition time of the proposed system is much shorter than that of the conventional system.