AC compressor turns off and on when engine is idle
 

This just started recently, maybe a couple weeks after I got my starter replaced (not sure it is related).

But when my AC is on, and I roll to a stop, it sounds like the AC compressor is turning off and on rapidly when the engine is at idle. I believe this is the case, because it makes the same sound and change in engine idle as when the AC button is pressed. So fearing it will damage something, I turn off the AC when at stop lights, which prevents this from happening, but having to do this is annoying.

When driving the AC does not do this.

I am not sure if it would resolve it, but it seems like my engine idle is very low and rough to begin with. I was thinking if I could increase the idle it may resolve the AC issue. But I don't know how to do this.

Check whether the condenser fan runs when the A/C is turned on.

Also check whether the condenser is clogged with bugs and road debris.

What model year? Models before 2001, if the fan works, next check the IACV. When the engine idles too low for any reason, the computer will drop the A/C off rapidly to prevent stalling.

sorry, its a 2000 Civic DX

You might also check the Freon level. The compressor will turn on and off if it is low or too high.