This hex specifically says instantly (which is quite ambiguous).
Effect: The witch can instantly cause her hair (or even her eyebrows) to grow...
But, hexes are typically activated with a standard action as default:
Unless otherwise noted, using a hex is a standard action that does not provoke an attack of opportunity.
Maybe it can be activated as a free action?
Like most witch hexes without a stated activated time, the activation time of the witch hex prehensile hair is a standard action. While the unfortunate use of the word instantly in the hex's description has led to debate on this topic on the Paizo messageboards (e.g. this thread from 2011), creative director James Jacobs clarifies in this 2012 exchange that activating the hex is, in fact, a standard action:
Question: What kind of action is activating a witch Prehensile Hair? it is a hex, so apparently it is a standard action, but the power say they grow instantly.…
Answer: Using the ability is a standard action, but the strands themselves lengthen as appropriate to do the task they need to do without you needing to spend an action to do so.
While not a rules guy, Jacobs's clarification makes it clear that the hex prehensile hair jibes with the rest of the game rather than the description's use of the word instantly possessing secret mechanical value.
Despite the flavor text (instantly grows), there is no mention that this instant takes a swift or even a free action, and as such, remains a Standard Action, the default action to activate hexes.
Note that your hair grows once the hex is activated, and activating it takes a standard. Once its activated, the hair grows instantly.
