Abstract We report a study of the low-mass Class 0 multiple system VLA 1623AB in the Ophiuchus star-forming region, using H¹³CO⁺ (J = 3–2), CS (J = 5–4), and CCH (N = 3–2) lines as part of the ALMA Large Program FAUST. The analysis of the velocity fields revealed the rotation motion in the envelope and the velocity gradients in the outflows (about 2000 au down to 50 au). We further investigated the rotation of the circumbinary VLA 1623A disk, as well as the VLA 1623B disk. We found that the minor axis of the circumbinary disk of VLA 1623A is misaligned by about 12° with respect to the large-scale outflow and the rotation axis of the envelope. In contrast, the minor axis of the circumbinary disk is parallel to the large-scale magnetic field according to previous dust polarization observations, suggesting that the misalignment may be caused by the different directions of the envelope rotation and the magnetic field. If the velocity gradient of the outflow is caused by rotation, the outflow has a constant angular momentum and the launching radius is estimated to be 5–16 au, although it cannot be ruled out that the velocity gradient is driven by entrainments of the two high-velocity outflows. Furthermore, we detected for the first time a velocity gradient associated with rotation toward the VLA 16293B disk. The velocity gradient is opposite to the one from the large-scale envelope, outflow, and circumbinary disk. The origin of its opposite gradient is also discussed.