The present work proposes a cut-cell-based Direct Simulation Monte Carlo (DSMC) solver, for computing rarefied flows around complex geometries on Cartesian grids, wherein analytical expression for the surface of the immersed boundary (IB) is considered to evaluate cut-cell volume as well as to implement the particle–boundary interactions. Consequently the proposed DSMC solver models an accurate collision rate in the cut cells and ensures an analytically expressed IB-based implementation of the boundary conditions at thesurface of the immersed geometry, as in the IB methods for the continuum flows. Performance of the present Cartesian cut-cell-based DSMC solver is tested on a variety of rarefied gas flows around three complex geometries (cylinder, NACA 0012 airfoil and double-wedge airfoil) for various flow speeds (ranging from Ma = 2 to 10) and degrees of rarefication (varying from Kn = 0:25 to around 0.0032). Results of our computations on Cartesian grids show a very good agreement with the corresponding DSMC results in literature computed on body-fitted grids. Furthermore, the present results show a good agreement with the corresponding experimental data in the literature. Straightforward and analytically expressed IB-based implementation in the proposed DSMC solver can make it a natural choice for its coupling with an immersed boundary method (IBM)- based continuum solver for a novel coupled IBM–DSMC method for continuum–rarefied gas flows.