In this paper, we investigate an uplink communication scenario in which multiple users communicate with an access point (AP) employing non-orthogonal multiple access (NOMA). A pinching antenna, which can be activated at an arbitrary point along a dielectric waveguide, is deployed at the AP to dynamically reconfigure user channels. The objective is to maximize the system sum rate by jointly optimizing the pinching-antenna's position and the users' transmit powers. Two scenarios are considered: one without quality-of-service (QoS) guarantees, and the other with QoS guarantees. In the former case, users transmit at full power, and the antenna position is determined using the particle swarm optimization (PSO) algorithm. In the latter, an alternating optimization approach is adopted, where a low-complexity solution is derived for power allocation, and a modified PSO algorithm is applied to optimize the antenna position. Numerical results show that the proposed pinching-antenna-assisted system significantly improves the sum rate compared to the conventional fixed-antenna architecture. Furthermore, the NOMA-based approach consistently outperforms its TDMA-based counterpart. Finally, the proposed PSO-based method achieves near-optimal performance, particularly when the QoS constraints are moderate.