  Symmetry-protected topological superconductors (TSCs) can host multiple
Majorana zero modes (MZMs) at their edges or vortex cores, while whether the
Majorana braiding in such systems is non-Abelian in general remains an open
question. Here we uncover in theory the unitary symmetry-protected non-Abelian
statisitcs of MZMs and propose the experimental realization. We show that
braiding two vortices with each hosting $N$ unitary symmetry-protected MZMs
generically reduces to $N$ independent sectors, with each sector braiding two
different Majorana modes. This renders the unitary symmetry-protected
non-Abelian statistics. As a concrete example, we demonstrate the proposed
non-Abelian statistics in a spin-triplet TSC which hosts two MZMs at each
vortex and, interestingly, can be precisely mapped to a quantum anomalous Hall
insulator. Thus the unitary symmetry-protected non-Abelian statistics can be
verified in the latter insulating phase, with the application to realizing
various topological quantum gates being studied. Finally, we propose a novel
experimental scheme to realize the present study in an optical Raman lattice.
Our work opens a new route for Majorana-based topological quantum computation.
