Using recycled aggregate concrete in a composite slab among the most promising solutions to effectively increase the utilisation of construction and demolition waste concrete. Longitudinal shear failure is a critical failure mode of composite slabs directly determined by the interfacial bond behaviour between concrete and profiled steel decks. However, the influence of recycled concrete aggregate (RCA) on interfacial bond behaviour remains unclear. Thus, this study conducted a pull-out test on the interfacial bond behaviour of composite slabs on 15 groups of specimens considering variables of replacement ratios of RCA (0, 50, and 100%), water-to-cement ratios (0.31, 0.45, and 0.60), steel deck thicknesses (0.8, 1.0, and 1.2 mm), and steel deck rib heights (48 and 65 mm). The bond-slip curves for all slabs were obtained, based on which the failure mechanism and influence of RCA under different parameters were discussed. Finally, an empirical prediction model for the bond-slip curve was established on the basis of the test data. The results showed that (1) the failure mode of composite slabs was independent of RCA, while the decrease in the steel deck rib heights induced more cracks in the failed slabs; (2) incorporating RCA decreased the ultimate bond stress by 4%–20% and the stiffness by 8%–14%; (3) the influence of RCA was coupled with other parameters; and (4) the proposed model exhibited a good prediction capability for the bond-slip behaviour of steel-RAC composite slabs.