Fast and accurate Carrier Frequency Offset (CFO) estimation is a problem of significance in many multi-carrier modulation based systems, especially in uplink Orthogonal Frequency Division Multiple Access (OFDMA) where the presence of multiple users exacerbates the inter-carrier interference (ICI) and results in multi-user interference (MUI). In this paper, a new technique called partial FFT demodulation is proposed. Estimators for the CFO are derived by considering an approximated matched filter for each user, implemented efficiently using several FFTs operating on sub-intervals of an OFDM block. Through simulations, we demonstrate the feasibility and performance of the derived estimators, and discuss the associated trade-offs.