The current paper addresses the issue of estimating the user propagation delays, received carrier phase offsets and received amplitudes in an asynchronous DS-CDMA environment with frequency non-selective propagation channels. The proposed synchronizer is based on the expectation-maximization (EM) algorithm and takes benefit from the soft information delivered by the receiver which is of the turbo type. The performance of the proposed synchronizer is illustrated by simulation results. In particular, the mean and the mean squared error of the estimator, as well as the bit error rate reached by the synchronized system, are reported.