A robust and sustainable solution is required to tackle the ever-growing generation of construction waste worldwide. It has been known that construction waste yields concrete with substandard mechanical properties when used as a replacement for natural aggregates. With attributes like easy application and low cost, this study investigated the performance of low cost and easily available steel clamps to improve the compressive stress–strain properties of concrete fabricated with recycled concrete and brick aggregates. Results demonstrate that steel clamps effectively improved the stress–strain behavior of recycled aggregate concrete, and this improvement was more pronounced in concrete with a higher percentage of recycled aggregates. Steel clamps confinement increased the compressive strength by up to 242% and 252% for recycled concrete and recycled brick aggregate concrete, respectively, whereas the corresponding strain was increased by up to 448% and 414%, respectively. The stress–strain response of steel clamp-confined RAC was idealized into two branches: the first branch was assumed to be parabolic in shape till the peak strength, and a linear degrading branch was assumed for the post-peak region. Separate equations were proposed using regression analysis for peak strength, strain, initial modulus, and post-peak degradation modulus. The complete stress–strain curves of steel clamp-confined RAC were generated by utilizing existing equations. The proposed regression equations were combined with existing equations to generate complete stress–strain curves of steel clamp-confined RAC. In general, good agreement between experimental and predicted stress–strain curves was obtained.