Phonon angular momentum, characterized by circular or elliptical motion of atoms, plays a decisive role in diverse phenomena, ranging from the phonon Hall effect, phonon magnetic moment, Einstein-de Haas effect, Weyl phonons, and driven chiral phonons. The phonon modes with an antisymmetric Raman tensor, which carry an intrinsic phonon angular momentum in a pseudovector symmetry channel, have been overlooked in the past in the chiral phonon community. Here, we report the detection of this type of phonon mode using polarization-resolved Raman spectroscopy. We observe a phonon at 266cm⁻¹ in the antiferromagnetic chiral phase of Cr₂O₃ in the A₂-pseudovector symmetry channel. This A₂ mode's frequency and the elliptical motion are captured by first-principles phonon calculations, which treat both lattice and spins on an equal footing as 'slow' degrees of freedom. This mode gets Raman activity due to the presence of Cr vacancies in Cr₂O₃ that locally break the twofold rotational symmetry perpendicular to the threefold axis. Our results provide a new way to detect the novel symmetry-forbidden A₂ phonon modes with an antisymmetric Raman tensor in a pseudovector symmetry channel.