Whenever I turn my air conditioning completely off, I can hear a weird knocking noise (it sounds like something hitting metal or something) coming from my engine bay. But whenever I turn a/c back on, the sound disappears. It doesn’t seem like the noise is affecting anything, as my a/c works just fine. I would just like to figure out what the noise is being caused by. I’m not sure if the noise persists as I’m driving but it happens when the car is just idling. Any tips would be appreciated.

If you could take a video of the sound that would help a lot. Post it to youtube then put the link here and it will embed the video automatically.

here you go:

Ok so that arrhythmic ticking sound is almost definitely valve ticking noise, when you hit the AC it sounds like it raised the rpm just slightly which caused the ticking to go away. I bet if you watch the tach there's an rpm jump and if you have someone else replicate that just by pressing the gas slightly that the ticking would go away.

Take a long screw driver or stethoscope and listen for the noise around the engine bay. If it is the A/C compressor you should be able to hear the tick when the poke/prob the compressor body (careful of the belts).
Mine was dragging/rubbing slightly, but it was more of a soft grind, not an intermittent tick like yours is. What you can do is remove the clutch off of the A/C compressor and add a shim like I had to. Its one 8 or 10mm fastener, be careful as there are sometimes shims installed from factory. I think my A/C clutch bearing is starting to go out, thus it would rub, so I think I mainly band-aided it for now.
Check your pulleys and other accessories for play/noise too.