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In this paper, the optimal carrier frequency offset (CFO) and channel estimator for an orthogonal frequency-division multiple-access (OFDMA) uplink based on a joint maximum-likelihood (ML) criterion is derived. Direct implementation of the resultant estimation scheme is challenging due to the need for a multidimensional exhaustive search in multi-CFO estimation. To solve this problem, an optimization theorem is exploited, and a computationally efficient method using an importance sampling technique is proposed. Without the need to provide an initial estimate, the proposed estimator guarantees the generation of the global optimal solution. Simulation results clearly verify the effectiveness of the proposed estimation scheme.