Orthogonal frequency division multiple access (OFDMA) systems, such as IEEE 802.16e/m and 3GPP Long Term Evolution (LTE), require significantly large signaling overhead for delivering small-sized delay-sensitive traffic such as voice over IP (VoIP) service. It may result in a significant decrease in the spectral efficiency. In order to overcome this drawback, recently, a persistent scheduling scheme has been standardized in standard bodies. In order to reduce the signaling overhead, the modulation and coding scheme (MCS) is set to be fixed during a burst period for the persistent scheduling procedure and an incomplete transmission, if it occurs, is recovered by a hybrid automatic repeat request (HARQ) scheme. In this paper, considering the HARQ retransmissions, we propose a rate selection scheme for the persistent scheduling satisfying given quality of service (QoS) requirements. In our proposed rate selection scheme, we consider two important factors which were not considered in previous HARQ-related work: time-correlations of the wireless channel in the HARQ retransmissions and the resource usage of signaling overhead. Numerical results show that the proposed rate selection scheme can efficiently enhance the utilization of radio resources compared to the conventional schemes.