Rate-splitting multiple access (RSMA) has attracted a lot of attention as a general and powerful multiple access scheme. In the uplink, instead of encoding the whole message into one stream, a user can split its message into two parts and encode them into two streams before transmitting a superposition of these two streams. The base station (BS) uses successive interference cancellation (SIC) to decode the streams and reconstruct the original messages. Focusing on the packet transmission reliability, we investigate the features of RSMA in the context of hybrid automatic repeat request (HARQ), a well-established mechanism for enhancing reliability. This work proposes a HARQ scheme for uplink RSMA with different retransmission times for a two-user scenario and introduces a power allocation strategy for the two split streams. The results show that compared with non-orthogonal multiple access (NOMA) and frequency division multiple access (FDMA), RSMA outperforms them in terms of error probability and power consumption. The results show that RSMA with HARQ has the potential to improve the reliability and efficiency of wireless communication systems.