Abstract: While self-centering rocking structures can reduce seismic damage and enhance seismic resilience, they may exhibit significant torsional responses. Linked twin-cylinder fluid inertial dampers can selectively increase the torsional stiffness of the structures after rocking while keeping their lateral stiffness characteristics unchanged, offering a viable method for torsional vibration control. First, a theoretical analysis of the damper identifies the optimal damping effect source through the velocity index and proposes an inertia mass amplification coefficient suitable for the laminar flow regime. A subsequent monobloc test confirms the theoretical formulae for the damping force from the frictional head loss and from the inertia mass under laminar flow, validating the theoretical predictions. A torsional vibration control system for the self-centering rocking column structure using the linked twin-cylinder fluid inertial damper is thusly proposed. Finite element simulation case studies further verify the effectiveness of the system.