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Partonic collectivity is one of the necessary signatures for the formation of quark-gluon plasma in high-energy nuclear collisions. Number of constituent quarks (NCQ) scaling has been observed for hadron elliptic flow v_{2} in top energy nuclear collisions at the Relativistic Heavy Ion Collider and the LHC, and this has been theoretically suggested as strong evidence for partonic collectivity. In this Letter, a systematic analysis of v_{2} of π^{±}, K^{±}, K_{S}^{0}, p, and Λ in Au+Au collisions at sqrt[s_{NN}]=3.2, 3.5, 3.9, and 4.5 GeV, with the STAR experiment at the Relativistic Heavy Ion Collider, is presented. NCQ scaling is markedly violated at 3.2 GeV, consistent with a hadronic-interaction dominated equation of state. However, as the collision energy increases, a gradual evolution to NCQ scaling is observed. This beam-energy dependence of v_{2} for all hadrons studied provides evidence for the onset of dominant partonic interactions by sqrt[s_{NN}]=4.5  GeV.