Idle issues

Camry '02 (4cylinder) engines rocks when turning AC on, changed engine mounts, cleand trotlle body still having idle problems. Need help

I’d look at the Idle Air Control valve. They usually don’t need to be replaced but it could be gunked up. It comes off pretty easily. Shake it out and spray it with some throttle body cleaner.
It may still be something else but cleaning the IACV is a cheap thing to try.

Is this a single rock that occurs as the compressor kicks on or a continuous rocking while the compressor is running? When the compressor is running, is the idle speed the same or is it lower?

Check this out.