A hair-styling appliance includes a first and second arm pivotably mounted between a spaced-apart and a closed configuration; a reservoir mounted on the first arm and intended for containing a fluid to be vaporised; a vaporisation device mounted on the first arm and configured for generating vapour; a fluid-conveying element attached to the reservoir and configured for conveying fluid contained in the reservoir to the vaporisation device. The reservoir is movably mounted between a vaporisation position in which the vaporisation device is configured for vaporising the fluid conveyed by the fluid conveying element and an inoperative position. The hair-styling appliance includes an actuating element mounted on the second arm and configured for moving the reservoir from the inoperative position to the vaporisation position when the first and second arms are moved from the spaced-apart configuration to the closed configuration.