Recently, in light of the success of quantum computers, research teams have actively developed quantum-inspired computers using classical computing technology. One notable success story is the Ising Machine (IM), which excels in efficiently solving NP-hard combinatorial optimization problems (COPs) in various domains such as finance, drug development, and logistics. However, IMs may encounter the von Neumann bottleneck due to significant data transfers between computing and memory units. To tackle this issue, processing-in-memory (PiM) leveraging resistive random-access memory (ReRAM) has emerged as a potential solution. Nonetheless, existing ReRAM-based IM accelerators face challenges stemming from non-ideal ReRAM devices and the limited flexibility in selecting solver algorithms. To overcome these limitations, we propose ReAIM, a ReRAMbased Adaptive Ising Machine, co-designed with an adaptive parameter search algorithm to dynamically select an appropriate solver algorithm and hardware/software parameters for the target COP. Based on our in-depth analysis, ReAIM accounts for the impact of both software parameters, such as the choice of local search algorithm and the number of spin flips, and hardware characteristics, including ReRAM-induced errors. Its reconfigurable architecture and optimized mapping/scheduling strategies enable efficient execution of the adaptive algorithm across various COPs, even for large-scale problems. Compared to the state-of-the-art SRAM-based IM accelerator, ReAIM achieves a $2.2 \times$ shorter time-to-solution (TTS), showcasing superior hardware performance without compromising solution quality.