We describe a morphological imprint of magnetization found when considering the relative orientation of themagnetic field direction with respect to the density structures in simulated turbulent molecular clouds. This imprintwas found using the Histogram of Relative Orientations (HRO), a new technique that utilizes the gradient tocharacterize the directionality of density and column density structures on multiple scales. We present results ofthe HRO analysis in three models of molecular clouds in which the initial magnetic field strength is varied, but anidentical initial turbulent velocity field is introduced, which subsequently decays. The HRO analysis was appliedto the simulated data cubes and mock-observations of the simulations produced by integrating the data cube alongparticular lines of sight. In the three-dimensional analysis we describe the relative orientation of the magnetic fieldBwith respect to the density structures, showing that: (1) the magnetic field shows a preferential orientation parallelto most of the density structures in the three simulated cubes, (2) the relative orientation changes from parallelto perpendicular in regions with density over a critical densitynTin the highest magnetization case, and (3) thechange of relative orientation is largest for the highest magnetization and decreases in lower magnetization cases.This change in the relative orientation is also present in the projected maps. In conjunction with simulations, HROscan be used to establish a link between the observed morphology in polarization maps and the physics included insimulations of molecular clouds.