Within the framework of 3D resistive magnetohydrodynamic, we simulate the formation of a plasma jet with the morphology, upward velocity up to 130 km s −1 , and time-scale formation between 60 and 90 s after beginning of simulation, similar to those expected for type II spicules. Initial results of this simulation were published in paper by, e.g. González-Avilés et al. (2018), and present paper is devoted to the analysis of transverse displacements and rotational-type motion of the jet. Our results suggest that 3D magnetic reconnection may be responsible for the formation of the jet in paper by González-Avilés et al. (2018). In this paper, by calculating times series of the velocity components v x and v y in different points near to the jet for various heights we find transverse oscillations in agreement with spicule observations. We also obtain a time-distance plot of the temperature in a cross-cut at the plane x = 0.1 Mm and find significant transverse displacements of the jet. By analysing temperature isosurfaces of 10 4 K with the distribution of v x , we find that if the line-of-sight (LOS) is approximately perpendicular to the jet axis then there is both motion towards and away from the observer across the width of the jet. This red-blue shift pattern of the jet is caused by rotational motion, initially clockwise and anti-clockwise afterwards, which could be interpreted as torsional motion and may generate torsional Alfvén waves in the corona region. From a nearly vertical perspective of the jet the LOS velocity component shows a central blue-shift region surrounded by red-shifted plasma.