From what I know, you can use a Spell Scroll if the spell is on your class's list.
Rangers gain the Spellcasting feature at second level (getting spell slots to cast 1st-level spells at that point), but they are technically Rangers already at level 1.
So, could a level 1 Ranger cast spells from Ranger spell scrolls? (If so, I suppose he would need to roll even for first-level Ranger spell scrolls.)
The answer to this question also applies for level 1 Paladins.
Yes, but the Ranger must pass an ability check to cast the spell
That's the constraint; is it on my class spell list? But here's the kicker:
At level 1, you can't normally cast a level 1 spell. Therefore, the Ranger must pass (DC = 11) ability check for a level 1 spell to be cast from the scroll. (And DC = 12 for a 2d level scroll spell, etc)
You have already learned how to cast spells
In the Ranger class description, this entry implies that spell casting ability is already present before the first spell slots arrive at level 2
That's a little bit of textual analysis, and possibly hair splitting. It doesn't say "after" or "when" you reach 2d level. The "you have learned" points to something that has already happened. There is still the chance to fail, per the scroll rules text cited above.
Thanks and acknowledgement must go to @NautArch, and to @DavidCoffron and to @GreySage for a detailed discussion of this whole thing in chat to kick this point around.
It is worth noting that the attempt to meet or beat the 11/12, whatever DC requires a decision on what spell casting modifier to add to the roll: 0 or the Wisdom modifier.
Either go with 0 + proficiency - per GreySage's answer - under the theory that the spell casting feature hasn't "switched on", or add the wisdom modifier + proficiency under the theory that the Ranger being a spell casting class will use the spell casting modifier.
The DM can rule either way, but should consider why to add, or not to add, the Wisdom modifier before making that ruling.