Circularly polarized light can open a topological gap in a gapless Dirac system, creating a Floquet-Chern insulator. However, its Berry curvature has not been directly resolved. Here we use circular-dichroism time- and angle-resolved photoemission spectroscopy (Tr-ARPES) to map the light-induced Berry curvature of Floquet-Bloch states on the surface of Bi₂Se₃. By comparing spectra for opposite helicities of the mid-infrared pump, we isolate the induced geometric response. We observe alternating-sign Berry-curvature features at Floquet gaps that repeat at intervals set by the pump photon energy and redistribute with pump field strength in agreement with calculations for a periodically driven Dirac Hamiltonian. Both the induced Berry-curvature and the Floquet Dirac gap decay faster than the replica intensity, showing that spectral replicas can persist even after coherent Floquet hybridization weakens. These results establish momentum-resolved Berry-curvature mapping as a direct probe of light-induced topology and coherent Floquet band formation.