Geographic registration (geo-registration) is a crucial foundation for augmented reality (AR) map applications. However, existing methods encounter difficulties in aligning spatial data with the ground surface in complex outdoor scenarios. These challenges make it difficult to accurately estimate the geographic north orientation. Consequently, the accuracy and robustness of these methods are limited. To overcome these challenges, this paper proposes a rotation-invariant estimation method for high-precision geo-registration in AR maps. The method introduces several innovations. Firstly, it improves the accuracy of generating heading data from low-cost hardware by utilizing Real-Time Kinematic GPS and visual-inertial fusion. This improvement contributes to the increased stability and precise alignment of virtual objects in complex environments. Secondly, a fusion method combines the true-north direction vector and the gravity vector to eliminate alignment errors between geospatial data and the ground surface. Lastly, the proposed method dynamically combines the initial attitude relative to the geographic north direction with the motion-estimated attitude using visual-inertial fusion. This approach significantly reduces the requirements on sensor hardware quality and calibration accuracy, making it applicable to various AR precision systems such as smartphones and augmented reality glasses. The experimental results show that this method achieves AR geo-registration accuracy at the 0.1-degree level, which is about twice as high as traditional AR geo-registration methods. Additionally, it exhibits better robustness for AR applications in complex scenarios.