For the concentrating solar power (CSP) applications, the supercritical carbon dioxide (s-CO2) power cycle is beneficial in many aspects, including high cycle efficiencies, reduced component sizing, and potential for the dry cooling option. More research is involved in improving this technology to realize the s-CO2 cycle as a candidate to replace the conventional power conversion systems for CSP applications. In this study, an isothermal compressor, a turbomachine which undergoes the compression process at constant temperature to minimize compression work, is applied to the s-CO2 power cycle layout. To investigate the cycle performance changes of adopting the novel technology, a framework for defining the efficiency of the isothermal compressor is revised and suggested. This study demonstrates how the compression work for the isothermal compressor is reduced, up to 50%, compared to that of the conventional compressor under varying compressor inlet conditions. Furthermore, the simple recuperated and recompression Brayton cycle layouts using s-CO2 as a working fluid are evaluated for the CSP applications. Results show that for compressor inlet temperatures (CIT) near the critical point, the recompression Brayton cycle using an isothermal compressor has 0.2-1.0% point higher cycle thermal efficiency compared to its reference cycle. For higher CIT values, the recompression cycle using an isothermal compressor can perform above 50% in thermal efficiency for a wider range of CIT than the reference cycle. Adopting an isothermal compressor in the s-CO2 layout can imply larger heat exchange area for the compressor which requires further development.