The lowest-lying 1(01) <-- 0(00) transition of para-H(2)D(+) and 1(11) <-- 0(00) of ortho-D(2)H(+) has been detected by the enhancement of the D/H isotope exchange reaction in collisions with p-H2 upon rotational excitation. These are the first pure rotational spectra of molecular ions by action spectroscopy. For this purpose, a cryogenic multipole ion trap has been combined with narrow-band tunable radiation sources operating in the 1.25 to 1.53 THz range. The low temperature of the ions allows us to determine the astronomically important transitions with a relative precision of Delta nu/nu=10(-8). While the 1 476 605.708(15) MHz line center frequency for the o-D(2)H(+) transition agrees very well with previous unpublished work, the 1 370 084.880(20) MHz line center frequency for the p-H(2)D(+) transition deviates by 61 MHz. Potential future applications of this new approach to rotational spectroscopy are discussed.