This study presents a novel design methodfor determining the tensile load-bearing capacity of a rivet nut connection with an aluminium alloy profile. The method, developed based on the requirements of standards LVS EN 1993-1-8:2025, LVS EN 1999-1-1:2023, and LVS EN1999-1-4:2023, incorporates checks on the aluminium profile web’s shear strength, rivet and rivet nut capacities, thread strength, and profile web buckling. Twenty-five laboratory specimens across five groups—with web thicknesses ranging from 2 mm to 5 mm and utilising rivet nuts made of AISI 303 1.4305 stainless steel and AW 5052 H32 aluminium alloy—were tested. The aluminium profiles were grade AW 6060 T66. Results show that using stainless steel rivet nuts increased the elastic-stage load-carrying capacity (Fp0.2) by 18.33% and the ultimate load capacity (Fm) by 15.89% compared to aluminium alloy nuts. The proposed design algorithm, validated by experimental tests and finite element method (FEM) analyses using Dlubal RFEM 6 (v. 4), predicts tensile resistance within a 10% accuracy. The study identifies pull-out of the aluminium profile wall as a critical failure mechanism, emphasising its inclusion to avoid overestimating connection capacity. This method provides a practical and reliable design tool for tensile load-bearing rivet nut connections in aluminium structural systems.