In this letter, we investigate the performance of Max Minimum Fairness (MMF) for uplink Rate-Splitting Multiple Access (RSMA) in short-packet communications. Specifically, considering a Single-Input Single-Output (SISO) Multiple Access Channel (MAC), we optimize the transmit power allocation between the splitting user messages to maximize the minimum rate among users with Finite Blocklength (FBL) constraints. To tackle this problem, we propose a Successive Convex Approximation (SCA)-based approach. Additionally, we introduce a low-complexity scheme to design the decoding order at the receiver. Numerical results show that RSMA outperforms conventional transmission schemes such as Non-orthogonal Multiple Access (NOMA) in terms of MMF.