In this study, we introduce a novel laser imaging technique, named as scanning laser-induced fluorescence (SLIF), designed to quantify the time-averaged three-dimensional mixing behavior of inclined dense jets with and without swirl. SLIF builds upon the established planar laser-induced fluorescence (LIF) method, which is widely used for experimental studies on buoyant jets in the laboratory. Unlike traditional LIF which is typically stationary, SLIF involves towing a light sheet obliquely in a back-and-forth manner through the flow domain to generate a volumetric scan. Simultaneously, an imaging camera is also towed at an oblique angle to capture the LIF images synchronously, allowing for comprehensive three-dimensional concentration measurements within the scanned volume. Compared to previous scanning approaches, SLIF is able to provide spatial measurements without the concern of defocusing due to the fixed relative distance between the laser sheet and camera. For validations, laboratory experiments with turbulent non-buoyant jets were first conducted. The results demonstrated good agreement with existing literature data. Subsequently, SLIF was applied to quantify the mixing characteristics of 45-degree inclined dense jets with and without swirl. In particular, the experimental results confirmed that SLIF offers valuable visualizations of mixing patterns in complex swirling situations that require three-dimensional volumetric scanning. Moreover, the volumetric measurements also enable the extraction of oblique sections across the inclined dense jet, facilitating the analysis of concentration distributions at various offset planes. This capability is crucial for enhancing the understanding of three-dimensional mixing processes for inclined dense jets particularly with swirl.