Requirements
To qualify to become an arcane archer, a character must fulfill all the following criteria.Base Attack Bonus: +6.
Feats: Point Blank Shot, Precise Shot, Weapon Focus (longbow or shortbow).
Spells: Ability to cast 1st-level arcane spells.
If one were inclined to avoid a spellcasting class, four levels of Rogue, taking the Minor Magic and Major Magic talents would allow the character to qualify for the class... However, Arcane Archer grants "+1 level of existing class".
How would this be resolved?
No. Minor Magic and Major Magic will not qualify you for it. See the Spell Like Ability FAQ for details.
Rogues no longer qualify for Arcane Strike anymore either.