Cordless curling iron containing a gas cartridge, butane fueled curling irons
Quantity limits: One per person in carry-on baggage only.
A safety cover must be securely fitted over the heating element. The device must be protected from accidental activation.
Gas refills (spare cartridges) are not permitted.
Electric curling irons and hair straighteners (cord plugs into an electric outlet) are not restricted.
See the regulation: 49 CFR 175.10(a)(6)
For international flights check with your airline as international regulations may vary from domestic regulations.