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We study the rotation effects of the hot and dense QCD matter in a non-perturbative regime by the gauge/gravity duality. We use the gravitational model that is designated to match the state-of-the-art lattice data on the thermal properties of (2+1)-flavor QCD and predict the location of the critical endpoint and the first-order phase transition line at large baryon chemical potential without rotation. After introducing the angular velocity via a local Lorentz boost, we investigate the thermodynamic quantities for the system under rotation in a self-consistent way. We find that the critical temperature and baryon chemical potential associated with the QCD phase transition decrease as the angular velocity increases. Moreover, some interesting phenomena are observed near the critical endpoint. We then construct the 3-dimensional phase diagram of the QCD matter in terms of temperature, baryon chemical potential, and angular velocity. As a parallel investigation, we also consider the gravitational model of $SU(3)$ pure gluon system, for which the 2-dimensional phase diagram associated with temperature and angular velocity has been predicted. The corresponding thermodynamic quantities with rotation are investigated.