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This paper addresses the challenge of achieving Differential Privacy (DP) in Federated Learning (FL) under the partial-participation setting, where each machine participates in only some of training rounds.While earlier work achieved optimal performance and efficiency in full-participation scenarios, these methods could not extend effectively to cases with partial-participation.Our approach addresses this gap by introducing a novel noise-cancellation mechanism that ensures privacy without compromising convergence rates or computational efficiency.We analyze our method within the Stochastic Convex Optimization (SCO) framework and demonstrate that it achieves optimal performance for both homogeneous and heterogeneous data distributions.This work broadens the applicability of DP in FL, providing a practical and efficient solution for privacy-preserving learning in distributed systems with partial participation.