We identify stellar tidal debris from the ω Centauri (ω Cen) system among field stars in the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey via chemical tagging using a neural network trained on APOGEE observations of the ω Cen core. We find a total of 463 ω Cen debris candidates have a probability P > 0.8 of sharing common patterns in their chemical abundances across a range of individual elements or element combinations, including [C+N], O, Mg, Al, Si, Ca, Ni, and Fe. Some debris candidates show prograde or retrograde disk-like kinematics, but most show kinematics consistent with the accreted halo, showing high radial actions, JR, values. We find that a sample of Gaia-Sausage-Enceladus (GES) members are chemically distinct from the ω Cen core, suggesting that ω Cen is associated with an independent merger event shaping the Milky Way halo. However, a connection between GSE and ω Cen cannot be ruled out. A detailed comparison with N-body simulations indicates that the ω Cen progenitor was a massive dwarf galaxy (≳108M⊙). The existence of a metal-poor high-α chemically homogeneous halo debris is also reported.