In this paper, an efficient closed-loop link adaption scheme consisting of adaptive modulation and coding as well as adaptive precoding is proposed for the 3GPP LTE-A uplink. The uplink envisaged in the LTE-A cellular network will support precoded multi-rank transmission from the users and have base stations with advanced non-linear receivers. Our proposed scheme considers one such advanced receiver, namely, the turbo successive interference cancelation (Turbo-SIC) receiver. The main difficulty in designing link adaptation schemes for these advanced non-linear receivers is that the soft-outputs of such receivers cannot be simply modeled using a scalar Gaussian channel characterized by a signal-to-interference-plus-noise ratio (SINR). To circumvent this difficulty, we employ SINRs corresponding to an ordered hard-decision SIC receiver, that can be explicitly expressed in closed form. The proposed scheme accurately predicts the turbo SIC performance and results in a perfect match between the predicted and actually simulated performance in terms of block error rate (BLER) and the spectrum efficiency. Realistic and extensive simulations reveal that it provides the highest actual spectrum efficiency compared to other competing schemes.