This paper proposes a novel cross-layer scheduling scheme for a single-cell orthogonal frequency division multiple access (OFDMA) wireless system with partial channel state information (CSI) at transmitter (CSIT) and heterogeneous user delay requirements. Previous research efforts on OFDMA resource allocation are typically based on the availability of perfect CSI or imperfect CSI but with small error variance. Either case consists to typify a non tangible system as the potential facts of channel feedback delay or large channel estimation errors have not been considered. Thus, to attain a more realistic resolution our cross-layer design determines optimal subcarrier and power allocation policies based on partial CSIT and individual user's quality of service (QoS) requirements. The simulation results show that the proposed cross-layer scheduler can maximize the system's throughput and at the same time satisfy heterogeneous delay requirements of various users with significant low power consumption.