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Field-aligned currents (FACs) flowing in the auroral ionosphere are a complex system of upward and downward currents, which play a fundamental role in the magnetosphere–ionosphere coupling and in the ionospheric heating. Here, using data from the ESA-Swarm multi-satellite mission, we studied the complex structure of FACs by investigating sign-singularity scaling features for two different conditions of a high-latitude substorm activity level as monitored by the AE index. The results clearly showed the sign-singular character of FACs supporting the complex and filamentary nature of these currents. Furthermore, we found evidence of the occurrence of a topological change of these current systems, which was accompanied by a change of the scaling features at spatial scales larger than 30 km. This change was interpreted in terms of a sort of symmetry-breaking phenomenon due to a dynamical topological transition of the FAC structure as a consequence of FACs and substorm current wedge intensification during substorms.