Applying a novel action spectroscopic technique in a 4 K cryogenic ion-trap instrument, the molecule c-C3H2D+ has been investigated by high-resolution rovibrational and pure rotational spectroscopy for the first time. In total, 126 rovibrational transitions within the fundamental band of the ν1 symmetric C-H stretch were measured with a band origin centred at 3168.565 cm-1, which were used to predict pure rotational transition frequencies in the ground vibrational state. Based on these predictions, 16 rotational transitions were observed between 90 and 230 GHz by using a double-resonance scheme. These new measurements will enable the first radio-astronomical search for c-C3H2D+.