Is there an FAA regulation to switch off the air-conditioning during take off?
It is not an FAA regulation to have the air conditioning off during takeoff and/or landing, however some manufacturers require it, in which case the pilot is legally obligated to comply with it.

I have flown two aircraft (both jets) which required it to be off:


Some of the Learjets require the AC to be off for both takeoff and landing because it uses a high draw electrical motor to drive the compressor, and when it cycles off and on it causes electrical spikes which can cause problems with the anti-skid system.
Some of the Dassault Falcon jets require the AC to be off for takeoff (actually, they automatically turn it off, but if the automatic system is inoperative the MEL requires turning it off manually) for performance reasons.  Since the AC is these aircraft is using bleed air off of the engine compressor as a source, allowing the air to continue through the engine instead increases thrust.


I know that many airliners have the option to takeoff with it on or off for performance reasons, and provide performance charts or adjustments for both.