Is there a power armor training perk in fallout new Vegas?

Yes. You can acquire power armor training from the Brotherhood Elder in the Hidden Valley bunker, to do so you must either find access to the bunker by convincing a Ranger in an adjacent bunker to leave or having Veronica as a companion. Once in, you most perform a series of quest to prove your worth and then you are rewarded with power armor training and a set of power armor.

Also if you complete Arcade Gannon's personal quest 'For Auld Lang Syne' you will receive a suit of Remnants Power Armour (either gifted by Daisy or taken from members who you may be forced to kill) and the skill to use it will automatically be granted.