We demonstrate rotational cooling of the silicon monoxide cation via optical pumping by a spectrally filtered broadband laser. Compared with diatomic hydrides, SiO^{+} is more challenging to cool because of its smaller rotational interval. However, the rotational level spacing and the large dipole moment of SiO^{+} allows for direct manipulation by microwaves, and the absence of hyperfine structure in its dominant isotopologue greatly reduces demands for pure quantum state preparation. These features make ^{28}Si^{16}O^{+} a good candidate for future applications such as quantum information processing. Cooling to the ground rotational state is achieved on a 100 ms timescale and attains a population of 94(3)%, with an equivalent temperature T=0.53(6) K. We also describe a novel spectral-filtering approach to cool into arbitrary rotational states and use it to demonstrate a narrow rotational population distribution (N±1) around a selected state.