You can't make a Sneak Attack with the Piercing Arrow
Sneak Attack description is:
Beginning at 1st level, you know how to strike subtly and exploit a foe’s distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.
You must use a finesse or a ranged weapon, no problems here — an Arcane Archer use shortbow or longbow with the Piercing Arrow, both shortbow and longbow are ranged weapons.
"Hit with an attack" means to hit (match or overcome the target's AC) with an attack roll. More information here - What counts as an attack?
Does the Piercing Arrow require the attack roll? In UA, its description was:
When you attack with this arrow, it fires forward in a line that is 1 foot wide and 30 feet long. You make a separate attack using your Arcane Arrow against each creature in that line.
However, in XGtE the description was changed:
Piercing Arrow. You use transmutation magic to give your arrow an ethereal quality. When you use this option, you don’t make an attack roll for the attack
You don't make an attack roll for the attack, so you don't hit with an attack, so no Sneak Attack additional damage can be applied.
Jeremy Crawford clarifies this:
@JeremyECrawford How does Assassinate, Sneak Attack, and Arcane Archer's Seeking/Piercing Shot play together if it's the first attack of a combat?
If a feature, such as Sneak Attack and Assassinate, does something special when an attack hits, that special effect doesn't occur if there's no attack roll that hits. #DnD