In topological insulator (TI) surface states the spin is locked to the momentum. In the presence of a Zeeman field, this produces an anomalous ${\varphi }^0$ shift in the current-phase relation of Josephson junctions which have a TI as a weak link. In this work, we investigate the anomalous Josephson effect in junctions where a HgTe nanowire is the weak link between Nb leads. We observe a giant anomalous ${\varphi }^0$ shift, which we attribute to the presence of a single Fermi contour in the HgTe surface states. Furthermore, by rotating an in-plane magnetic field, we can map the spin texture in momentum space. Our analysis reveals that the spin is not strictly orthogonal to the momentum, but exhibits a significant deviation of 19°. These findings demonstrate that the anomalous Josephson effect is a highly sensitive probe for the spin texture in generic chiral 2D systems.