Forty-nine angular distributions for states in /sup 23/Na up to 16.6 MeV in excitation energy populated by the /sup 12/C(/sup 15/N,..cap alpha..)/sup 23/Na reaction have been measured in 400 keV intervals for bombarding energies from 36.0 to 39.2 MeV. Hauser-Feshbach calculations have been made to suggest spins for most of the states observed. Shell-model predictions were used to guide the suggestions for positive-parity spin state locations. High-spin members of three rotational bands, K/sup ..pi../= 3/2/sup +/, 1/2/sup +/, and 1/2/sup -/, were suggested and average moment-of-inertia parameters were extracted from the band systematics.