Can dark neutrino interactions phase out the Hubble tension?

New interactions of neutrinos can stop them from free streaming even after the weak interaction freeze-out. This results in a phase shift in the cosmic microwave background (CMB) acoustic peaks which can alleviate the Hubble tension. In addition, the perturbations in neutrinos do not decay away on horizon entry and contribute to metric perturbation enhancing the matter power spectrum. We demonstrate that this acoustic phase shift can be achieved using new interactions of standard left-handed neutrinos with dark matter without changing the number of effective relativistic degrees of freedom. Using Planck CMB and the WiggleZ galaxy survey (k <= 0.12h Mpc(-1)) data, we demonstrate that in this model the Hubble tension reduces to approximately 2.1 sigma. Our model predicts potentially observable modifications of the CMB B modes and the matter power spectrum that can be observed in future datasets.