This letter investigates a fluid antenna (FA)-assisted integrated sensing and communication (ISAC) system, with joint antenna position optimization and waveform design. We consider enhancing the sum-rate maximization (SRM) and sensing performance with the aid of FAs. Although the introduction of FAs brings more degrees of freedom for performance optimization, its position optimization poses a non-convex programming problem and brings great computational challenges. This letter contributes to building an efficient design algorithm by the block successive upper bound minimization and majorization-minimization principles, with each step admitting closed-form update for the ISAC waveform design. In addition, the extrapolation technique is exploited further to speed up the empirical convergence of FA position design. Simulation results show that the proposed design can achieve state-of-the-art sum-rate performance with at least 60% computation cutoff compared to existing works with successive convex approximation (SCA) and particle swarm optimization (PSO) algorithms.