I turn on my AC the RPM does not increase?

Hello,

When the A/C gets turned on the ECM increases the RPMs by couple of hundred, it sends a signal to the idle air control valve for that task.
If the IAC becomes dirty it might not able able to adjust the RPMs when needed. As the air will be restricted due to build up.
So check the IAC and clean if necessary, many times cleaning the IAC will fix this issue.

https://www.2carpros.com/articles/how-a-idle-air-control-valve-works
https://www.2carpros.com/articles/idle-air-control-valve-service

I have attached diagrams for your reference.

Please let me know of any questions.

Thank you.