This paper addresses, for the first time, the uplink performance optimization of multi-user pinching-antenna systems, recently developed for next-generation wireless networks. By leveraging the unique capabilities of pinching antennas to dynamically configure wireless channels, we focus on maximizing the minimum achievable data rate between devices to achieve a balanced trade-off between throughput and fairness. An effective approach is proposed that separately optimizes the positions of the pinching antennas and the resource allocation. The antenna positioning problem is reformulated into a convex one, while a closed-form solution is provided for the resource allocation. Simulation results demonstrate the superior performance of the investigated system using the proposed algorithm over corresponding counterparts, emphasizing the significant potential of pinching-antenna systems for robust and efficient uplink communication in next-generation wireless networks.