This paper proposes a spectrum-efficient spatio-temporal array-receiver (STAR) for multi-carrier CDMA systems named MC-STAR. First, we derive a new post-correlation model for MC-CDMA that supports both the MT-CDMA and MC-DS-CDMA air-interfaces. Based on this model, we introduce a new multi-carrier receiver with rapid and accurate joint synchronization in time and frequency. We also exploit the intrinsic subcarrier correlation to improve the channel identification and the synchronization operations. We analyze the performance of MC-STAR in an unknown time-varying Rayleigh channel with multipath, carrier offset and cross-correlation between subcarrier channels. Simulation results confirm the accuracy of the joint time/frequency synchronization. They also confirm that for each MC-STAR configuration there exists an optimum number of subcarriers which results in maximum throughput. A higher number of subcarriers increases the inter-carrier interference while a lower number of subcarriers reduces the frequency gain. With four receiving antennas and five MT-CDMA subcarriers in 5 MHz bandwidth, MC-STAR provides about 1.2 bps/Hz at low mobility for DBPSK, i.e., an increase of 30% in spectrum efficiency over DS-CDMA.