When two nodes communicate using in-band full-duplex (FD) with orthogonal frequency division multiplexing (OFDM), the self-interference (SI) and desired signals experience a time and frequency misalignment problem. In this article, we introduce the effect of timing and frequency offsets in FD systems. A conventional FD node simultaneously receives two signals: the desired signal and the SI. The FD node then synchronizes based on the desired signal, and the SI is distorted by timing and frequency offsets. These timing and frequency offsets break orthogonality and create inter-symbol interference and inter-channel interference that degrade the performance of the self-interference cancellation (SIC). To address this, we design a modified digital SIC approach that considers the timing and frequency offset and synchronizes the desired signal and the SI in consecutive order.