Equipped with an adaptive beamformer, existing adaptive array code acquisition still relies on the correlator structure. Due to the inherent property of the associated serial-search scheme, its mean acquisition time is large, especially in strong interference environments. In this paper, we propose a novel adaptive filtering scheme to solve the problem. The proposed scheme comprises two adaptive filters, an adaptive spatial and an adaptive temporal filter. With a specially designed structure, the spatial filter can act as a beamformer suppressing interference, while the temporal filter can act as a code-delay estimator. A mean squared error (MSE) criterion is proposed such that these filters can be simultaneously adjusted by a stochastic gradient descent method. The performance as well as the convergence behavior of the proposed algorithm are analyzed in detail. Closed-form expressions for optimum filter weights, optimum beamformer signal-to-interference-plus-noise ratio (SINR), steady-state MSE, and mean acquisition time are derived for the additive white Gaussian noise (AWGN) channel. Computer simulations show that the mean acquisition time of the proposed algorithm is much shorter than that of the correlator-based approach, and the derived theoretical expressions are accurate.