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We present an analysis of the molecular specific angular momentum–mass (jH2 − MH2) relation using a sample of 51 nearby disc galaxies from the PHANGS-ALMA survey with deep high-resolution molecular gas rotation curves and surface density profiles. For the very first time, using a statistical sample, we report the discovery of a well-defined jH2 − MH2 relation. We quantify the scaling law by fitting a power law with a Bayesian framework, finding jH2 ∝ MH20.53. This slope closely resembles the well-known stellar j*–M* (Fall) relation, highlighting the dynamical connection between molecular gas and stars. We show that the jH2 − MH2 relation cannot be fully explained by analytic models of disc stability, but instead is well recovered with more complex physics as implemented in the S<ns0:sc>HARK</ns0:sc> semi-analytical model. These findings demonstrate the power of our novel jH2 − MH2 relation in testing galaxy evolution theories and in setting new constraints for models and simulations that reproduce a realistic interstellar medium. Additionally, our findings provide a critical benchmark for upcoming high-redshift studies of molecular gas kinematics, offering a local baseline to study the evolution of cold gas dynamics across cosmic time.