  We have analyzed the angular momentum of the molecular cloud cores in the
Orion A giant molecular cloud observed in the N2H+ J = 1-0 line with the
Nobeyama 45 m radio telescope. We have measured the velocity gradient using
position velocity diagrams passing through core centers, and made sinusoidal
fitting against the position angle. 27 out of 34 N2H+ cores allowed us to
measure the velocity gradient without serious confusion. The derived velocity
gradient ranges from 0.5 to 7.8 km/s/pc. We marginally found that the specific
angular momentum J/M (against the core radius R) of the Orion N2H+ cores tends
to be systematically larger than that of molecular cloud cores in cold dark
clouds obtained by Goodman et al., in the J/M-R relation. The ratio beta of
rotational to gravitational energy is derived to be beta = 10^{-2.3+/-0.7}, and
is similar to that obtained for cold dark cloud cores in a consistent
definition. The large-scale rotation of the integral-shaped filament of the
Orion A giant molecular cloud does not likely govern the core rotation at
smaller scales.
