[RPG] Can an Assassin use Assassinate with ranged spell attacks

No, critical hits must be linked with attack rolls.

I checked with Jeremy Crawford on Twitter and he says that critical hits must come from attack rolls:

@JeremeyECrawford No, since only attack rolls can score critical hits.

In response to @Kevinaskevin Can my Rogue's Assassinate cause my Wand of Magic Missile to crit against surprised creatures?

You should read the full conversation between he and I to get more detail.

Critical hits come up in the PHB on pgs. 194 & 196. As I see it the PHB pg. 194 text doesn't imply that critical hits are exclusive to attack rolls:

If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter.

PHB 196 describes critical hits but never uses the words "attack roll". Reading the text above someone new to DND could reasonably assume there are other causes of critical hits.

Despite this, Jeremy made it clear that the game designers intended critical hits and attack rolls to be linked.

If you hit, it is already considered a critical hit

This is the case regardless of whether you then roll a natural 20 or not.

When the Rogue is assassinating a surprised target, it will be a critical hit regardless of what the roll of the d20 is, providing of course you still beat the target's AC.

So no, the critical hits do not stack