Are electric cigarettes allowed through security?

You can carry them with you in carry on luggage or handbag, will not be allowed in checked in luggage if it has lithium ion battery.

Yes they are.

Electronic cigarettes, vape pens, and other vaping devices are only allowed in carry-on bags. When a carry-on bag is checked at the gate or plane side, all electronic cigarette and vaping devices, along with any spare lithium batteries, must be removed from the bag and kept with the passenger in the aircraft cabin.