The wind turbine side-side tower motion is known to be lightly damped. One viable active damping solution is realized by deploying individual pitch control (IPC) such that counteracting blade forces are created to alleviate the tower fatigue loading caused by this motion. Existing IPC methods for side-side tower damping in the literature, such as linear quadratic regulator and lead-lag controller, cannot accommodate direct optimization and tradeoff tunings of the wind turbine economic performance. In this work, a novel side-side tower damping IPC strategy under a convex economic model predictive control (CEMPC) framework is therefore developed to address these challenges. The main idea of the framework lies in the variable transformation in power and energy terms to obtain linear dynamics and convex constraints, over which the economic performance of the wind turbine is maximized with a globally optimal solution in a receding horizon manner. The effectiveness of the proposed method is showcased in a high-fidelity simulation environment under both steady and turbulent wind cases. Lower fatigue damage on the side-side tower bending moment is attained with an acceptable level of pitch activities, negligible impact on the blade loads, and minor improvement on the power production.