Renewable energy powered cognitive radio (CR) network has gained much attention due to its combination of the CR's spectrum efficiency and the renewable energy's "green" nature. In the paper, we investigate the delay-optimal data transmission in the renewable energy aided CR networks. Specifically, a primary user (PU) and a secondary user (SU) share the same frequency in an area. The SU's interference to the PU is controlled by interference-signal-ratio (ISR) constraint, which means that the ISR at the PU receiver (Rx) should be less than a threshold. Under this constraint, the renewable energy powered SU aims to minimize the average data buffer delay by scheduling the renewable allocations in each slot. A constrained stochastic optimization problem is formulated when the randomness of the renewable arrival, the uncertainty of the SU's data generation, and the variability of the fading channel are taken into account. By analyzing the formulated problem, we propose two practical algorithms that is optimal for two special scenarios. And the two algorithms respectively give an upper and a lower bound for the general scenario. In addition, the availability of the PU's private information at the SU is discussed. Finally, numerical simulations verify the effectiveness of the proposed algorithm.