Standardized alignment of the embryo in three-dimensional (3D) ultrasound images aids prenatal growth monitoring by facilitating standard plane detection, improving visualization of landmarks and accentuating differences between different scans. In this work, we propose an automated method for standardizing this alignment. Given a segmentation mask of the embryo, Principal Component Analysis (PCA) is applied to the mask extracting the embryo's principal axes, from which four candidate orientations are derived. The candidate in standard orientation is selected using one of three strategies: a heuristic based on Pearson's correlation assessing shape, image matching to an atlas through normalized cross-correlation, and a Random Forest classifier. We tested our method on 2166 images longitudinally acquired 3D ultrasound scans from 1043 pregnancies from the Rotterdam Periconceptional Cohort, ranging from 7+0 to 12+6 weeks of gestational age. In 99.0% of images, PCA correctly extracted the principal axes of the embryo. The correct candidate was selected by the Pearson Heuristic, Atlas-based and Random Forest in 97.4%, 95.8%, and 98.4% of images, respectively. A Majority Vote of these selection methods resulted in an accuracy of 98.5%. The high accuracy of this pipeline enables consistent embryonic alignment in the first trimester, enabling scalable analysis in both clinical and research settings. The code is publicly available at: https://gitlab.com/radiology/prenatal-image-analysis/pca-3d-alignment.