Ion-molecule reactions proceed with highly rotational-state-specific rate coefficients and are amenable to stereodynamical control at low temperatures. We introduce a scheme to control cold ion-molecule chemistry with microwaves based on the coherent transfer of molecular rotational-state populations. We use a merged-beam approach to reach collision energies in the range from ∼0 to k_{B}×10 K for the reaction between He^{+} and rotationally cold CO molecules (T_{rot}≈3 K) and manipulate the rotational-state population of CO using microwave pulses. We achieve reaction inhibition by up to ∼40% with microwave pulses resonant with pure-rotational transitions in CO, unambiguously demonstrating a nonthermal mechanism for microwave-assisted chemistry.