One of the challenges in spacecraft attitude control is that the dynamics model is nonlinear, uncertain, and often costly to identify. To address this issue, this paper proposes a new Data-Enabled Predictive Control (DeePC) method based on sparse kernelized learning using Fully Independent Training Conditional (FITC) approximation, which utilizes behavioral system theory to learn unknown dynamics and predict future angular velocities of the spacecraft. The key advantage of the proposed method is that it can avoid complex modeling and reduce computational loads compared to the existing methods. Moreover, the hyperparameters of the kernel, together with the inducing points, are optimized via maximum log-likelihood approach to further improve the prediction accuracy and lower computational cost. Numerical simulations in spacecraft attitude stabilization and tracking scenarios validate the effectiveness of the proposed method.