This letter investigates the performance of uplink rate splitting multiple access (RSMA) in a two-user scenario, addressing an under-explored domain compared to its downlink counterpart. Specifically, we derive closed-form expressions for the outage probability, throughput, and asymptotic outage behavior of uplink users, considering imperfect channel state information at the receiver (CSIR) and successive interference cancellation (SIC). We validate the accuracy of these derived expressions using Monte Carlo simulations. Our findings reveal that at low transmit power levels, imperfect CSIR significantly affects system performance more severely than SIC imperfections. However, as the transmit power increases, the impact of imperfect CSIR diminishes, while the influence of SIC imperfections becomes more pronounced. Moreover, we highlight the impact of the rate allocation factor on user performance. Finally, our comparison with non-orthogonal multiple access (NOMA) highlights the outage performance trade-offs between RSMA and NOMA. RSMA proves to be more effective in managing imperfect CSIR and enhances performance through strategic message splitting, resulting in more robust communication.