The O-RAN architecture standardized by the O-RAN Alliance does not support the latency requirement of real-time fifth-generation (5G) edge intelligence, typically at a msec level. In this paper, we proposed a deep reinforcement learning (DRL) packet scheduler framework to manage users with different quality of service (QoS) requirements. The DRL framework uses an advantage actor-critic (A2C) algorithm, referred to as a QoS-A2C scheduler. The developed QoS-A2C scheduler is then proposed as an O-RAN real-time App at the edge network. Simulation results show that the latency of the App is at $\mu\sec$ level. It also improves the QoS satisfaction level by more than 50% compared to other DRL-based scheduler schemes.