Carrier mobility is a key parameter determining the response speed of charge carriers to electric fields in nanoelectronic devices. This study aims to explore the charge carrier transport properties of monolayer IrSCl and IrSI. Using first-principles calculations based on density functional theory (DFT), we systematically investigated the electronic structure and transport properties of monolayer IrSCl and IrSI. 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). Evaluating the bandgap 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 (PBE) and 1.58 eV (HSE06), while those for monolayer IrSI are 0.23 eV (PBE) and 1.36 eV (HSE06). We further investigated the effects of biaxial tensile strain on the bandgap, revealing that the bandgap of IrSCl and IrSI decreases with increasing strain, reaching 0.05 eV and 0.01 eV (PBE) at a strain of 6%, indicating a strain-induced transition to metallic behavior. Based on deformation potential theory and the Boltzmann transport equation, we calculated the carrier mobilities of monolayer IrSCl and IrSI. The predicted maximum carrier mobility for monolayer IrSCl at room temperature is 407.77 cm ²V ^-1s ^-1, while that for monolayer IrSI is 202.64 cm ²V ^-1s ^-1. Additionally, results from the Boltzmann transport equation show that the highest mobilities for IrSCl and IrSI are 299.15 cm ²V ^-1s ^-1and 286.41 cm ²V ^-1s ^-1, respectively. These findings suggest that both IrSCl and IrSI possess favorable electronic and transport properties, making them promising candidates for future applications in two-dimensional nanoelectronic devices. Notably, the combination of a moderate bandgap and high carrier mobility at room temperature indicates their potential use in 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.