  We consider an explanation of CDF II W bosom mass anomaly by $Z-Z'$ mixing
with $U(1)_R$ gauge symmetry under which right-handed fermions are charged. It
is found that $U(1)_R$ is preferred to be leptophobic to accommodate the
anomaly while avoiding other experimental constraints. In such a case we
require extra charged leptons to cancel quantum anomalies and the SM charged
leptons get masses via interactions with the extra ones. These interactions
also induce muon $g-2$ and lepton flavor violations. We discuss muon $g-2$,
possible flavor constraints, neutrino mass generation via inverse seesaw
mechanism, and collider physics regarding $Z'$ production for parameter space
explaining the W boson mass anomaly.
