In this paper, we propose an online blind source separation (BSS) method that is robust against the self-rotation of microphone arrays. Online auxiliary-function-based independent vector analysis (OIVA) is one of the promising methods for real-time BSS. One major issue of real-time BSS is robustness against the movements of sources or microphones. Parameter re-estimation is necessary if such changes occur during processing. OIVA is robust against smooth movements of sources and achieves high separation performance. However, OIVA should perform better against rapid movements of microphones. In this study, we exploit sound field interpolation (SFI) for circular microphone arrays (CMAs) with OIVA. SFI cancels out the rotation of a CMA, enabling us to apply BSS without parameter re-estimation. We propose two methods: a combination of SFI and OIVA for preprocessing and a method using parameter transformations for practical applications. Simulation experiments confirmed that SFI improves the robustness of OIVA in situations where the microphone is rotating.