Each time you gain an indicated level of Arcane Archer, choose a class which grants arcane spellcasting and in which you already have at least one level. When looking at the "spells per day" and "spells known" tables, start with the number of actual levels you have in that class, and add the number of times you've chosen that class in step one. Similarly, when determining ranges, durations, and other level-dependent effects, use that higher caster level.
So, your Sorc 3/Ranger 5 wants to start taking Arcane Archer levels. She gains enough XP to attain level 8, and takes her first AA level. The AA "Spells Per Day" column has a dash, so spell casting is unaffected. She does gain Enhance Arrows, of course.
A while later, she gains 9th level and takes her second AA level. AA's "Spells Per Day" column has "+1 level of existing class", so she has to choose an arcane spell-casting class in which she has levels; her only choice is Sorcerer, so she chooses Sorc. AA gives her Imbue Arrow, and she treats her Sorc level as 4 to determine spells per day (ie., she gains 2nd level Sorc spells (plus whatever she gets from her CHA)), spells known (ie., she learns one cantrip and one 2nd level spell), caster level-dependent effects (eg., range, duration, number of magic missiles, concentration check modifiers, etc.). She does not, however, increase the power of any Bloodline Powers she may have. Were she to have Wizard levels, she could choose to increase her Wizard caster level in the same way, but she would not get the two spells per level for free (ie., she'd have to add spells to her spellbook by transcribing them from a scroll or another spellbook), nor would her familiar or bonded item gain in power.
If a wholly different character were going into Arcane Archer with two classes which offered arcane spellcasting, they could choose which class to advance at each AA level. There are 7 levels at which he could increase an arcane caster level, so he could add 7 to one class and 0 to another, or 6 and 1, 5 and 2, or 4 and 3; similarly, he could choose to do so in any order he wished: 3 of one class, one of the other, then 3 of the first again, for example.
Curving Shot can potentially be used every round thanks to Magic Arrow
Jeremy Crawford, official 5e rules designer, clarifies the interaction of the two features here on Twitter:
Arcane Archer; Curving Shot in Xanathars: Can be used every round for the cost of a bonus action cause all arrows fired from L or S Bow can be considered magical by 7th level? y/n?
Yes.
As you point out, the Magic Arrow feature lets any nonmagical arrow fired by the Arcane Archer from a shortbow or longbow be treated as magical during the attack. Curving Shot lets you use a bonus action to reroll a miss with a magic arrow to attack a different target within 60 feet of the missed target.
Together, this means that as long as you're shooting a longbow or shortbow and miss, you can use your bonus action to reroll that attack against a different target within 60 feet of the first.
If Magic Arrow's magic fades from the arrow immediately after it hits/misses, does that mean it stops being magical before the second attack?
Since you're "rerolling" the missed attack, I would personally interpret it as if the miss never actually missed, so the magic doesn't fade until after the rerolled attack is resolved. In universe, you're basically shooting at one target but your shot goes wide, and then the same arrow veers toward another target and either hits or misses.
Best Answer
Sorcerer has very little to offer an Arcane Archer-type build, with the exception of the Elemental Affinity feature from the Draconic Bloodline origin. Combined with Elemental Weapon, this allows you to add your Cha modifier as elemental damage to every shot you fire from your crossbow. The problem here is that Elemental Weapon is restricted to the Paladin class only.
So you have 3 options, explained below. Regardless of which you take, you'll be focussing on Cha and Dex, with Con as a secondary as usual. So you'll want to spend your 27 points in the 15,15,15,8,8,8 pattern. Then Half-Elf brings you up to 17 Cha, 16 Dex, 16 Con very neatly. Each build gets you 5 ability score increases over your career. You'll want to use these to bring Cha and Dex up to 20 and take Crossbow Expert so that you can dual-wield hand crossbows.
Option 1 is to take at least 9 levels of Paladin so you can cast Elemental Weapon. Then you'll want to bring Sorcerer up to 8 and Paladin up to 12 so you don't lose ability score increases. This isn't a terrible idea, as many of the Paladin's [X]ing Smite spells work with ranged attacks, making a pretty reasonable Arcane Archer. With the Oath of Devotion's Sacred Weapon ability, you could also add your Cha modifier to your attack rolls. That said, many of the Paladin's class features don't work with ranged attacks, and it's not exactly an Arcane Archer anyway. Also, you'll have to have Str 13 to multiclass Paladin; so your starting ability scores will be 15,15,13,12,8,8 with Half-Elf making it 17 Cha, 16 Dex, 13 Str, 13 Con. (You only lose out on Con, so it's not too bad.) The main thing this option gets you that the other 2 don't is the cool Smite spells that add damage and additional effects to your crossbow attacks, just like an Arcane Archer.
Option 2 is to take 6 levels of Lore Bard for Additional Magical Secrets, which you can use to gain access to Elemental Weapon. You could use the other magical secret to get Branding Smite for that Arcane Archer flavour. Then, you'll want to take 5 levels in a martial class for Extra Attack; I'd strongly recommend Fighter, so that you can take Fighter 6 and not lose an ability score increase. Once you're Sorcerer 6/Bard 6/Fighter 6, take 2 more levels in whichever of these 3 classes you like to get your last ability score increase. This option is the least focussed, but you get the Archery fighting style and Improved Critical for your crossbow, so it's got a slight edge with the crossbow you're looking to optimize. This can also get you Arcane Archer-ing the fastest, since your combo comes into play at level 12.
The final option is to take 10 levels of Valor Bard, and use Magical Secrets to get Elemental Weapon. The other magical secret could be used for Banishing Smite, Branding Smite, or Staggering Smite for more Arcane Archer flavour. While this doesn't sound as good as Lore Bard, you get Extra Attack for free along the way. Then you should probably take Sorcerer up to 8 and Bard up to 12 to keep all your ability score increases. This option gets you the most powerful spellcasting of all of them, but you don't get the Archery fighting style.