Both reconfigurable intelligent surface (RIS) and non-orthogonal multiple access (NOMA) are treated as promising technologies for future wireless communications. However, the performance gain achieved by the traditional passive RIS-aided NOMA system is limited due to the double-fading effect for the base station (BS)-RIS-user channel. In this letter, a sum rate maximization problem for active RIS-aided uplink multi-antenna NOMA system is studied, in which the reflecting elements (REs) of active RIS can manipulate the phase shifts and amplify the amplitudes of incident signals. To tackle the formulated sum rate maximization problem, the original optimization problem is decomposed into three subproblems, i.e., the equalizer optimization, the power allocation, and the active RIS beamforming design. Simulation results show that the proposed active RIS-aided NOMA system can effectively improve sum rate compared with several benchmark schemes.