Carrier mobility is a key parameter determining the response speed of charge carriers to electric fields in nanoelectronic devices. This study aims to investigate the charge carrier transport properties of monolayer IrSCl and IrSI. Using first-principles calculations based on density functional theory, we systematically investigate the electronic structure and transport properties of monolayer IrSCl and IrSI. The phonon dispersion calculations indicate that both IrSCl and IrSI exhibit no imaginary frequencies, confirming their structural stability. Furthermore, molecular dynamics simulations demonstrate that these materials maintain thermal stability at room temperature (300 K). The evaluation of the bandgap by using the Perdew-Burke-Ernzerhof (PBE) functional and the hybrid HSE06 functional shows that both IrSCl and IrSI are indirect bandgap semiconductors. The bandgap values for monolayer IrSCl are 0.37 eV and 1.58 eV under the PBE functional and the HSE06 functional, respectively, while those for monolayer IrSI are 0.23 eV and 1.36 eV under the PBE functional and the HSE06 functional, respectively. We further investigate the effects of biaxial tensile strain on the bandgap. The bandgap of IrSCl and IrSI decrease with the increase of strain, respectively reaching 0.05 eV and 0.01 eV under the PBE functional at a strain of 6%, indicating a strain-induced transition to metallic behavior. According to deformation potential theory and the Boltzmann transport equation, we calculate the carrier mobility for each of monolayer IrSCl and IrSI. The predicted maximum carrier mobility at room temperature is 407.77 cm ²/(V·s) for monolayer IrSCl, and 202.64 cm ²/(V·s) for monolayer IrSI. Additionally, the results from the Boltzmann transport equation show that the highest mobility is 299.15 cm ²/(V·s) for IrSCl and 286.41 cm ²/(V·s) for IrSI. These findings suggest that both IrSCl and IrSI possess favorable electronic and transport properties, thus they have become promising candidates for future applications in the field of two-dimensional nanoelectronic devices. Notably, the combination of a moderate bandgap and high carrier mobility at room temperature indicates their potential applications in the fields of transistors, sensors, and other electronic components. This study provides valuable insights into the material properties of IrSCl and IrSI, contributing to the design of novel two-dimensional materials for electronic applications.