Single carrier frequency division multiple access (SC-FDMA), a modified form of orthogonal frequency division multiple access (OFDMA), is a promising technique for high data rate and low peak-to-average power ratio for uplink communications in cellular networks. However, similar to OFDMA, SC-FDMA also suffers from carrier frequency offset (CFO). Particularly, in the presence of multiple users, the uplink SC-FDMA introduces multiple CFOs. The CFOs must be estimated and compensated before demodulating the signal to minimize the inter-carrier interference (ICI) and ensure the efficiency of the SC-FDMA uplink system. In this paper, we propose a method for multi-user CFOs estimation that exploits the property of minimum variance of signal amplitudes at the receiver across different subcarriers. It utilizes the mean and variance of the output magnitude based on its probability density function. The variance approaches minimum value when CFO is fully compensated. The CFO estimation performance is evaluated on the basis of simulation and comparison with other methods over frequency selective fading channel environments.