Tactile servoing is an effective approach to enabling robots to safely interact with unknown environments. One of the core problems in tactile servoing is to robustly converge the contact features to the desired ones via a dedicated controller. This paper proposes a Data-Driven Model Predictive Controller (DDMPC) to compute the motion command given the previous interaction experience and feature deviations in tactile space. Compared with the manually designed PID-based controller, the proposed controller depends on the sound control theory and its convergence is guaranteed from a computational perspective. It is applied to the balancing control of a rolling bottle on a robotic forearm covered by a custom tactile sensor array. The real experiment demonstrates the superior robustness of the proposed approach and shows its great potential for other tactile servoing scenarios with measurement noise, which is inevitable for current tactile sensors.