We present the kinematic analysis of a sub-sample of 82 galaxies at 0.75 < z < 1.2 from our new survey HR-COSMOS aimed to obtain the first statistical sample to study the kinematics of star-forming galaxies in the treasury COSMOS field at 0 < z < 1.2. We observed 766 emission line galaxies using the multi-slit spectrograph ESO-VLT/VIMOS in high-resolution mode (R = 2500). To better extract galaxy kinematics, VIMOS spectral slits have been carefully tilted along the major axis orientation of the galaxies, making use of the position angle measurements from the high spatial resolution HST/ACS COSMOS images. We constrained the kinematics of the sub-sample at 0.75 < z < 1.2 by creating high-resolution semi-analytical models. We established the stellar-mass Tully-Fisher relation at z ≃ 0.9 with high-quality stellar mass measurements derived using the latest COSMOS photometric catalog, which includes the latest data releases of UltraVISTA and Spitzer. In doubling the sample at these redshifts compared with the literature, we estimated the relation without setting its slope, and found it consistent with previous studies in other deep extragalactic fields assuming no significant evolution of the relation with redshift at z ≲ 1. We computed dynamical masses within the radius R2.2 and found a median stellar-to-dynamical mass fraction equal to 0.2 (assuming Chabrier IMF), which implies a contribution of gas and dark matter masses of 80% of the total mass within R2.2, in agreement with recent integral field spectroscopy surveys. We find no dependence of the stellar-mass Tully-Fisher relation with environment probing up to group scale masses. This study shows that multi-slit galaxy surveys remain a powerful tool to derive kinematics for large numbers of galaxies at both high and low redshift. Key words: galaxies: evolution / galaxies: kinematics and dynamics / galaxies: high-redshift / galaxies: statistics / surveys⋆ Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 083.A-0935.