We analyze the three-dimensional shapes and kinematics of the young star cluster population forming in a high-resolution griffin project simulation of a metal-poor dwarf galaxy starburst. The star clusters, which follow a power-law mass distribution, form from the cold phase interstellar medium with an initial mass function sampled with individual stars down to four solar masses at sub-parsec spatial resolution. Massive stars and their important feedback mechanisms are modeled in detail. The simulated clusters follow a surprisingly tight relation between the specific angular momentum and mass with indications of two sub-populations. Massive clusters (M cl 3 × 104 M o) have the highest specific angular momenta at low ellipticities ( ∼ 0.2) and show alignment between their shapes and rotation. Lower mass clusters have lower specific angular momenta with larger scatter, show a broader range of elongations, and are typically misaligned indicating that they are not shaped by rotation. The most massive clusters (M 105 M o) accrete gas and protoclusters from a ≲100 pc scale local galactic environment on a t ≲ 10 Myr timescale, inheriting the ambient angular momentum properties. Their two-dimensional kinematic maps show ordered rotation at formation, up to v ∼ 8.5 km s-1, consistent with observed young massive clusters and old globular clusters, which they might evolve into. The massive clusters have angular momentum parameters λ R ≲ 0.5 and show Gauss-Hermite coefficients h 3 that are anti-correlated with the velocity, indicating asymmetric line-of-sight velocity distributions as a signature of a dissipative formation process.