In-band full-duplex (IBFD) systems are expected to double the spectral efficiency compared to half-duplex systems, provided that loopback self-interference (SI) can be effectively suppressed. The inherent interference mitigation capabilities of the emerging fluid antenna system (FAS) technology make it a promising candidate for addressing the SI challenge in IBFD systems. This paper thus proposes a FAS-assisted self-interference cancellation (SIC) framework, which leverages a receiver-side FAS to dynamically select an interference-free port. Analytical results include a lower bound and an approximation of the residual SI (RSI) power, both derived for rich-scattering channels by considering the joint spatial correlation amongst the FAS ports. Simulations of RSI power and forward link rates validate the analysis, showing that the SIC performance improves with the number of FAS ports. Additionally, simulations under practical conditions, such as finite-scattering environments and wideband integrated access and backhaul (IAB) channels, reveal that the proposed approach offers superior SIC capability and significant forward rate gains over conventional IBFD SIC schemes.