This study presents the variation of shear characteristics of two different recycled aggregates when mixed with waste tire rubber crumbs. The two recycled aggregates were sourced from an authorized construction and demolition (C&D) waste plant and a demolished site of the Bus Rapid Transit System (BRTS) in Bhopal, Madhya Pradesh. The rubber crumbs were mixed with the recycled aggregates in varying proportions (0%, 5%, 10%, and 15% by weight of aggregates), and direct shear tests were conducted at 65% relative density. Results demonstrated that the optimal rubber crumb content was 10% for both the aggregate types, yielding maximum angle of friction values of 46.78° for C&D waste plant aggregates and 43.39° for BRTS waste aggregates. The integration of rubber crumbs enhances the frictional characteristics of the composite materials. These enhanced composites show considerable potential for sustainable construction applications, including backfill materials for retaining structures, granular column fillers for ground improvement, road sub-base layers, and reinforced soil structures. By managing demolition debris and used tire waste while developing composite materials with improved mechanical properties, the research contributes circular economy principles. This dual waste utilization technique reduces landfill burden and encourages resource recovery in the construction industry, providing an environmentally sustainable alternative.