Low cost Cu-based catalysts are attractive options in catalyzing higher alcohol synthesis (HAS) from syngas. Introducing isolated Rh single atoms into the surfaces of these Cu catalysts has the potential to dramatically improve the performance of these Cu-based catalysts. In this work, extensive density functional theory (DFT) calculations were performed with periodic slab models to systematically investigate the possibility of using Rh/Cu single-atom alloys (SAAs) as HAS catalysts. The mechanism of ethanol synthesis from syngas on the representative Rh/Cu(111) and Rh/Cu(100) surfaces was elucidated. All possible formation pathways of the C1 and C2 fragments leading to the ethanol main product, as well as the methane and methanol by-products were considered. Our calculations show that for ethanol formation, the C-C bond coupling is easier over the Rh/Cu SAA catalysts than pure Cu catalysts, suggesting that Rh/Cu SAA catalysts are more favorable for the formation of higher alcohols.