This paper proposes a new multiple access technique based on the millimeter wave lens-based reconfigurable antenna systems. In particular, to support a large number of groups of users with different angles of departures (AoDs), we integrate recently proposed reconfigurable antenna multiple access (RAMA) into non-orthogonal multiple access (NOMA). The proposed technique, named reconfigurable antenna NOMA (RA-NOMA), divides the users with respect to their AoDs and channel gains. Users with different AoDs and comparable channel gains are served via RAMA while users with the same AoDs but different channel gains are served via NOMA. This technique results in the independence of the number of radio frequency chains from the number of NOMA groups. Further, we derive the feasibility conditions and show that the power allocation for RA-NOMA is a convex problem. We then derive the maximum achievable sum-rate of RA-NOMA. Simulation results show that RA-NOMA outperforms conventional orthogonal multiple access (OMA) as well as the combination of RAMA with the OMA techniques.