The submillimeter-wave rotational spectra of CO(+), (13)CO(+) and C(18)O(+) in the v = 0 and 1 vibrational states were measured through a hollow cathode dc discharge in a cryogenic cell cooled to liquid nitrogen temperature. In addition, a few transitions of the main isotopic species have been measured between 1.1 and 1.3 THz. An updated isotopically invariant fit, including Born-Oppenheimer breakdown corrections, is presented: the derived set of independent molecular parameters, valid for all the isotopologues of the molecule included in the fit, allows to predict the rotational spectrum with calculated 1σ uncertainty of 280 kHz at 2 THz.