We present an investigation of the dependence of galaxy kinematics on the environment for a sample of 94 star-forming galaxies at $z\sim0.9$ from the ORELSE survey. ORELSE is a large photometric and spectroscopic campaign dedicated to mapping out and characterizing galaxy properties across a full range of environments in 15 fields containing large-scale structures (LSSs) in a redshift range of $0.6 < z < 1.3$. We constrained the rotation velocity for our kinematic sample in an ORELSE field, containing the SC1604 supercluster, by fitting high-resolution semi-analytical models to the data. We constructed the stellar-mass/B-band Tully-Fisher relation and found no dependence of the intrinsic scatter on both local and global environment. Moreover, we compared the stellar-to-dynamical mass ratio ($M_\ast/M_{dyn}$) of SC1604 galaxies to those residing in less dense local environment by leveraging data from the HR-COSMOS sample. We found that, at fixed stellar mass, SC1604 galaxies have $\sim30\%$ smaller dynamical masses on average. By comparing the distributions of the galaxy parameters that define $M_{dyn}$ (i.e., circular velocity and the characteristic radius $r_{2.2}$) between SC1604 and HR-COSMOS, we found that smaller dynamical masses are mostly caused by smaller $r_{2.2}$ for SC1604 galaxies. We also observed that SC1604 galaxies in general show $\sim20\%$ lower stellar specific angular momentum ($j_\ast$) with respect to the HR-COSMOS sample. Adopting literature estimates for (1) the excess rate of galaxy-galaxy mergers in intermediate/high-density environments and (2) the average amount of $j_\ast$ loss per merger event, we investigated the possibility that galaxy mergers are mainly responsible for the loss of angular momentum in higher density environments.