Two-dimensional materials are promising candidates for lithium ion battery anodes due to their large surface to volume ratio. The distorted T′ phase of the rhenium disulfide crystal makes the study of lithium binding more complex than for other two-dimensional materials with symmetric crystal structures. Here we explore the lithium ion storage capacity of monolayer rhenium disulfide by first-principles based calculations. We employ hardwareaccelerator-assisted high-throughput calculations, using a van der Waals density-functionaltheory based 'structure search' technique, to emulate the lithiation process. Exploring 2000 structures, each containing 49 to 98 atoms, we find the most stable lithiated structures for various lithium concentrations. We then design a delithiation algorithm and apply it to those lithiated structures for the estimation of the reversible specific capacity. Despite possessing high molar mass, a reasonably high specific capacity (214.13 mAh/g) and opencircuit voltage (0.8 V), in agreement with experimental results, make rhenium disulfide a promising alternative anode material.