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 large dipole moment of SiO+ allows 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 time scale 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 ($Npm1$) around a selected state.
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