Most works on reflecting-only intelligent reflecting surface (IRS) are based on the ideal phase shift model (IPSM), which assumes that the reflection amplitude is independent of the phase shift at each IRS element. However, due to hardware limitations of practical IRS circuits, practical IRS generally follows the practical phase shift model (PPSM), where the reflection amplitude is related to the phase shift. This paper analyzes the average block error rate (BLER) of PPSM-based IRSaided short-packet communication (SPC) with statistical channel state information over Rician fading. Because the optimal continuous phase shifts at the PPSM-based IRS are difficult to be explicitly solved, we first propose a deep deterministic policy gradient (DDPG) based algorithm to optimize the phase shift design. Then, we derive the average BLER of the considered IRS-aided SPC with the optimized reflection matrix. Finally, numerical and simulation results demonstrate that the IRS-aided SPC system with the proposed DDPG-based phase shifts outperforms the system with the IPSM-based optimal phase shifts. They also show that, different from the IPSM-based IRS, the optimal phase shifts at the PPSM-based IRS are related to the Rician factors.