You're using Ki arrow as a Ki power, most likely gained through Qinggong monk archetype. However, you still are casting this as a spell, which uses up your standard action. You have no way to apply Vital Strike to this spell at the same time, and so no, you wont be able to use Vital Strike in conjunction.
If instead you were using something like Blood Crow strike which allows you to make an unarmed strike or flurry of blows (at range) you could choose to Vital Strike with the single unarmed attacked. It'd be a waste, since you'd do more damage making a Flurry of Blows but you could do it.
Unfortunately Ki Arrow is worded differently and doesn't tell you to make an unarmed strike but just says you make a ranged attack roll and tells you the damage. It's not a standard attack action and just isn't comptaible.
OTOH, if you're asking about the zen archer's ki arrows ability, then yes. Ki arrow as a swift, Vital Strike as a standard.
My wife is currently pondering exactly this combo for her zen archer, for when she needs to move too far in a turn to flurry.
Honestly, thinking about it further it doesn't matter that he can cast Ki arrow as a swift action. It's the fact that it's a spell that specifies what the damage done is and has no capability to be combined with vital strike.
Blood Crow Strike as I mentioned above does, but would also be a bad idea to actually do.
The fact that you can Ki Arrow as a swift just means you could vital strike unarmed attack afterwards, but it wouldn't be a ranged attack as granted by Ki arrow.