A 13th level Rogue with the Thief archetype has the following feature:
Use Magic Device
By 13th level, you have learned enough about the workings of magic that you can improvise the use of items even when they are not intended for you. You ignore all class, race, and level requirements on the use of magic items.
And the DMG has this item, on page 211:
Wand of Paralysis (requires attunement by a spell caster)
Make a ranged attack roll against the creature using your spell attack bonus. On a hit, the target is paralyzed for 1 minute. At the end of each of the target's turns, it can repeat the saving throw.
So what is the spell save DC of a Rogue using their Use Magic Device feature, and what is their spell attack bonus?
A simple answer might be that Use Magic Device simply does not allow one to attune to this item.
I am personally not sure what to rule. My gut tells me it should be the player's choice of Intelligence or Wisdom, while still being on the fence as to whether they should be proficient or not. An alternative ruling would be just setting it to a DC of 15 like just about all the other wands and giving it a normal ranged attack roll via Dexterity.