It would likely be underpowered.
Let's compare the benefits of the arcane archer against the Hunter archetype.
As an Arcane Archer Ranger, you get free +1 ammo, an extra attack if you miss, a single skill proficiency, and what are effectively a handful of spells.
A Hunter Ranger could likely get a +1 weapon and the Volley ability is strictly better than the Curving Shot ability. Therefore, you're essentially comparing Arcane Shot against all of the other benefits of the other archetypes. It's up to you to determine whether it's worth it, but it doesn't seem like it to me.
You'd also experience some unevenness in your progression, because the typical ranger gets archetype abilities at levels 3, 7, 11, and 15, whereas the Arcane Archer gets new archetype abilities at 3,7, and 18 (though there are new arcane shot options between those).
This mismatch is due to developer intent
Rodney Thompson wrote an article detailing some of the developer intent behind each class. In it, he states that Fighters get most of their power from their base class:
Fighters gain most of their combat prowess from three characteristics of the class: being able to make up to four attacks per round; using Action Surge to grant quick bursts of combat potency; and having the highest number of Ability Score Improvement features...The fighter archetypes are largely meant to be different flavors of the base class, in which most of the fighter’s combat strength lies.
On the other hand, Rangers get most of their combat ability from their archetype:
Much of the ranger’s extra potency in combat comes from spells such as hunter’s mark and from the class features granted by the ranger archetypes.
Basically, Fighters have a strong base class and weaker archetypes, whereas Rangers have a weaker base class and stronger archetypes. By using the Ranger's base class and a Fighter archetype, you end up with the weaker aspects of both classes.