ABSTRACT We conducted 3D hydrodynamical simulations of common envelope evolution (CEE) of a neutron star (NS) or a black hole (BH) inside a red supergiant (RSG) envelope and find that the jets that we expect the NS/BH to launch during the CEE spin-up the common envelope. We find that when the NS/BH launches jets that are exactly perpendicular to the orbital plane (the jets are aligned with the orbital angular momentum) the jets deposit angular momentum to the envelope that is aligned with the orbital angular momentum. When the jets’ axis is inclined to the orbital angular momentum axis, so is the angular momentum that the jets deposit to the envelope. Such tilted jets might be launched when the NS/BH has a close companion when it enters the RSG envelope. We did not allow for spiralling-in and could follow the evolution for only three orbits. The first orbit mimics the plunge-in phase of the CEE, when the NS/BH rapidly dives in, while the third orbit mimics the self-regulated phase when spiralling-in is very slow. We find that the jets deposit significant amount of angular momentum only during the plunge-in phase. A post-CEE core collapse supernova explosion will leave two NS/BH, bound or unbound, whose spin might be misaligned to the orbital angular momentum. Our results strengthen an earlier claim that inclined-triple-star CEE might lead to spin-orbit misalignment of NS/BH-NS/BH binary systems.