This paper investigates the use of simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) for the uplink non-orthogonal multiple access (NOMA) to ensure the fairness among the users. To identify a more appropriate STAR-RIS protocol between the energy splitting (ES) and time switching (TS) for rate fairness, we optimize the power allocation and reflection/transmission coefficients of the STAR-RIS to maximize the minimum communication rate. The results show that, despite of energy loss of the ES protocol in the uplink, the uplink NOMA with the ES protocol outperforms that with the TS protocol. Nonetheless, the TS protocol can be employed for the uplink NOMA to reduce the receiver complexity at some slight loss in particular when the users in transmitting and reflecting regions are located symmetrically.