Unmanned aerial vehicles (UAVs) are increasingly deployed in mission-critical applications such as target tracking, where they must simultaneously sense dynamic environments, ensure reliable communication, and achieve precise control. A key challenge here is to jointly guarantee tracking accuracy, communication reliability, and control stability within a unified framework. To address this issue, we propose an integrated sensing, communication, and control (ISCC) framework for UAV-assisted target tracking, where the considered tracking system is modeled as a discrete-time linear control process, with the objective of driving the deviation between the UAV and target states toward zero. We formulate a stochastic model predictive control (MPC) optimization problem for joint control and beamforming design, which is highly non-convex and intractable in its original form. To overcome this difficulty, the target state is first estimated using an extended Kalman filter (EKF). Then, by deriving the closed-form optimal beamforming solution under a given control input, the original problem is equivalently reformulated into a tractable control-oriented form. Finally, we convexify the remaining non-convex constraints via a relaxation-based convex approximation, yielding a computationally tractable convex optimization problem that admits efficient global solution. Numerical results show that the proposed ISCC framework achieves tracking accuracy comparable to a non-causal benchmark while maintaining stable communication, and it significantly outperforms the conventional control and tracking method.