Blackcurrent,
The added load, when the A/C clutch is engaged, could cause a loose belt to "chirp" or screech.
This could also be caused by an excessive amount of resistance in the compressor (resistance to turning).
This can be caused by moisture in the system, refrigerant entering the compressor as a liquid, crap built up in the compressor, and/or bad bearings in the compressor.
If the oraface "o" rings are letting the liquid refrigerant get by to quickly, the liquid does not have time to "evaporate" (boil) in the evaporator core.
Note; The orafice is a restriction in the high pressure line that slows down the liquid refrigerant, that is, the gas (R-134a or R-12) that has been condensed into a liquid in the condenser. This gives the liquid that gets through to the evapoator core time to "evaporate". This evaporation, or boiling, is caused by the absorbing of warmth or heat.
Some of the liquid gets into the compressor cylinders, and the hydrolic pressure makes the compressor resist being turned. Have you checked your A/C system with pressure guages? High pressures on the low pressure side, and low pressures on the high side would indicate an oraface that is not working properly.
You should also look at the belt surface for "glazing". A belt that slips too often for too long will get "glazed", and should be replaced. Glaze - the belts friction surface becomes hardened, and sometimes has a shiney look to it.
These are just some thoughts on what might be causing your belt to "chirp" when you turn on the A/C, if it isn't just a loose belt! rangerj.