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Fetal brain biometry provides a quantitative basis for assessing prenatal growth and identifying congenital brain abnormalities. However, comprehensive assessment remains limited by labor-intensive manual measurements and automated models that lose accuracy across imaging sequences and institutions. We introduce BioTTA, an anatomically guided test-time adaptation framework that measures 11 fetal brain biometrics from reconstructed three-dimensional magnetic resonance images. BioTTA adapts pretrained models to individual unlabeled volumes using geometric consistency and atlas priors, without access to source images. In a retrospective study across five centers in China and Switzerland, BioTTA improved measurement accuracy across three out-of-distribution datasets and two network architectures. It reduced mean absolute measurement errors by 46-82% relative to the corresponding models without adaptation, achieving errors similar to those of supervised fine-tuning. Its measurements were mapped onto normative growth trajectories derived from expert annotations, enabling gestational-age-specific assessment through a web-based reporting platform. Across four disease cohorts, the platform achieved 82.1-95.0% accuracy in binary detection of ventriculomegaly or cerebellar abnormalities, with performance similar to that of a senior radiologist. BioTTA provides a practical foundation for standardized fetal brain biometry across heterogeneous imaging settings, supporting scalable prenatal growth assessment and quantitative evaluation of brain abnormalities.