In this paper,we investigate a novel wireless powered mobile edge computing (MEC) system assisted by pinching antennas (PAs), where devices first harvest energy from a base station and then offload computation-intensive tasks to an MEC server. As an emerging technology, PAs utilize long dielectric waveguides embedded with multiple localized dielectric particles, which can be spatially configured through a pinching mechanism to effectively reduce large-scale propagation loss. This capability facilitates both efficient downlink energy transfer and uplink task offloading. To fully exploit these advantages, we adopt a non-orthogonal multiple access (NOMA) framework and formulate a joint optimization problem to maximize the system's computational capacity by jointly optimizing device transmit power, time allocation, PA positions in both uplink and downlink, and radiation control. To address the resulting non-convexity caused by variable coupling, we develop an alternating optimization algorithm that integrates particle swarm optimization (PSO) with successive convex approximation. Simulation results demonstrate that the proposed PA-assisted design substantially improves both energy harvesting efficiency and computational performance compared to conventional antenna systems.