Turbulent structures detected in the edge plasma of fusion devices, often described as blobs, are generally believed to be responsible for confinement degradation. Recent experimental evidence and theories have suggested their filamentary electromagnetic nature. In this Letter the first direct experimental measurements of the parallel current density associated with turbulent structures in a fusion experiment are reported. The electromagnetic nature of structures is clearly shown by identifying the current filaments with a vortexlike velocity pattern and the associated pressure perturbation.