We provide novel random surface density functional theory (RSDFT) formulation in the case of geometric heterogeneous surfaces of solid media which is essential for the description of thermodynamic properties of confined fluids. The major difference of our theoretical approach from the existing ones is a stochastic model of solid surfaces which takes into account the correlation properties of geometry. The main building blocks are effective fluid-solid potentials developed in the work of Khlyupin and Aslyamov [J. Stat. Phys. 167, 1519 (2017)] and geometry-based modification of the Helmholtz free energy for Lennard-Jones fluids. The efficiency of RSDFT is demonstrated in the calculation of argon and nitrogen low temperature adsorption on real heterogeneous surfaces (BP280 carbon black). These results are in good agreement with experimental data published in the literature. Also several models of corrugated materials are developed in the framework of RSDFT. Numerical analysis demonstrates a strong influence of surface roughness characteristics on adsorption isotherms. Thus the developed formalism provides a connection between a rigorous description of the stochastic surface and confined fluid thermodynamics.