Space-borne antenna pointing is affected by uncertain disturbances like satellite attitude, structural flexibility, and manufacturing/installation errors. Understanding the effect of these uncertainties is crucial for antenna performance. The main contribution of this paper is the proposal of an uncertainty quantification (UQ) framework for antenna pointing performance that integrates the Global Sensitivity Analysis (GSA) method and Point Estimate Method (PEM), named the GSA-PEM Integrated Framework (GSA-PEM in short). This framework enables systematic analysis of how uncertain parameters (satellite attitude, manufacturing/installation errors, joint rotation, structural deformation, feed displacement, etc.) impact antenna pointing. It establishes a pointing model via coordinate transformation, utilizes the total-effect of the Sobol method to prioritize the key parameters for reliability analysis, and computes pointing performance statistics characteristic via PEM to evaluate pointing reliability. Two case studies are presented to validate the accuracy and efficiency of the proposed framework. Monte Carlo Simulation (MCS) and the Maximum Entropy method using the Fractional-order Moments (ME-FMs) are comparison methods. Results demonstrate that the proposed framework achieves a trade-off between accuracy and efficiency in assessing antenna pointing performance under parameter uncertainty.