To guarantee delay performances for timesensitive services in an orthogonal frequency-division multiple access passive optical network (OFDMA-PON), we propose a two-dimensional (i.e., subcarriers and time) upstream bandwidth allocation method based on interleaved polling with adaptive cycle time (IPACT). We first analyze its delay performance in terms of cycle time, i.e., the length of a polling cycle. Then, by setting the maximum polling cycle so as to guarantee timely transmissions for time-sensitive services, we identify the requirements, i.e., the maximum bandwidth allocation, the maximum number of allowed optical network units, and the optimum number of subcarriers, for upstream bandwidth allocation with delay guarantees. The proposed scheme is evaluated both numerically and via simulation.