I'd check the A/C system. Could be that the system is engaging the compressor too heavily, which then causes a heavier load than the engine was expecting, so the idle speed surges to keep the engine from stalling, and it just repeats.
It could be that the A/C system is low on oil, refrigerant, both oil and refrigerant, or just that the compressor is worn and the A/C clutch is just not working right.
Might need anything from a system recharge to a new compressor, or a whole new system if it's contaminated.
Hopefully it's a vacuum leak or something minor, but if it ONLY happens with the A/C on, it's likely the compressor or at least something A/C related.