Intelligent reflecting surface (IRS) has recently been recognized as a promising technology to enhance the energy and spectrum efficiency of wireless networks by controlling the wireless medium with the configurable electromagnetic materials. In this paper, we consider the downlink transmit power minimization problem for a IRS-empowered non-orthogonal multiple access (NOMA) network by jointly optimizing the transmit beamformers at the BS and the phase shift matrix at the IRS. However, this problem turns out to be a highly intractable non-convex bi-quadratic programming problem, for which an alternative minimization framework is proposed via solving the non-convex quadratic programs alternatively. We further develop a novel difference-of-convex (DC) programming algorithm to solve the resulting non-convex quadratic programs efficiently by lifting the quadratic programs into rank-one constrained matrix optimization problems, followed by representing the non-convex rank function as a DC function. Simulation results demonstrate the performance gains of the proposed method.