A Thief can use spell scrolls
The Sage Advice Compendium directly addresses this issue, so if you (or your DM, if you are a player) follow the official rulings, then they can use spell scrolls.
Does the Thief’s Use Magic Device feature allow them to use spell scrolls?
Yes. The intent is that a Thief can use spell scrolls with Use Magic
Device.
That just leaves the question of whether they have to make an ability check.
By a strict reading of RAW, the Thief doesn't need to make an ability check
Spell Scroll (DMG 200)
A spell scroll bears the words of a single spell, written in a mystical
cipher. If the spell is on your class's spell list, you can read the
scroll and cast its spell without providing any material components.
Otherwise, the scroll is unintelligible. [snip spell casting instructions]
The above describes 2 scenarios:
- The spell is on your class's spell list, so you can read the scroll and cast it without providing any material components.
- Otherwise, the scroll is unintelligible.
A strict reading of those two options means that for a thief, the scroll is unintelligible.
The description of spell scrolls continues:
If the spell is on your class's spell list but of a higher level than
you can normally cast, ... [snip rules for making the check]
Strictly reading of RAW, since the spell is not on the rogue's class spell list, then this paragraph does not apply, and so no ability check is required.
Are there any requirements or other checks a thief has to make?
That still doesn't completely answer the question of how they use the spell scroll. For that, we have to look at the description of the ability in question:
Use Magic Device (PHB 97)
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.
The Roguish archetype feature says that it says you improvise the use of items, and defines no conditions or checks on how to make it work. It simply lists out what you are allowed to ignore.
This led to this question in the first place, as what it says you can ignore doesn't directly apply to the spell scroll magic item description, but the official ruling clarifies that and doesn't lay out any additional conditions or requirements.
So, by strict reading of RAW (both rules as written and rulings as written), no ability check is required, nor any other requirement. The Thief simply can cast a spell from the unintelligible scroll.
Flavor
For an explanation of how it is possible to use an unintelligible scroll, you can just assume the Thief has watched enough magic users and memorized the words to any scrolls they found, much like Elan would be assumed to have learned from Vaarsuvius in The Order of the Stick, if he choose to multiclass.
Belkar: What about you? Throwing good levels after bad with another
bard level?
Elan: Maybe. I was also considering taking a level of
wizard, though.
Belkar: Wizard? Really? I didn't know you've been studying
wizardry.
Elan: I haven't been. But if I multiclass to wizard, it's retroactively
assumed that I've been looking over Vaarsuvius' shoulder this whole
time and taking notes about magic.
Belkar: But you haven't been.
Elan: But it's assumed that I
have been. Get it?
Belkar: Nice.
Or, you or your DM can flavor it however they would like.
A DM could reasonably call for a skill check
Now, while a strict RAW reading doesn't require any check, it does seem intended that unless your character can normally cast the spell that some type of check needs to be made. Otherwise, you get into a situation where a level 13 Thief Rogue can cast a level 8 or 9 spell scroll, whereas an equal leveled full caster needs to make a skill check.
While there could be some legitimate flavor reason for that to be the case, a reasonable DM could also see that situation and decide that a Thief should have to make an ability check, just like a character that has the spell on their spell list, but isn't of a high enough level.
Making an ability check to cast a spell from a scroll
Magic Items: Activating an item: Spells (DMG 141)
Some magic items allow the user to cast a spell from the item. [snip]
A magic item, such as certain staffs, may require you to use your own
spellcasting ability when you cast a spell from the item. [snip] If
you don't have a spellcasting ability -- perhaps you're a rogue with
the Use Magic Device feature -- your spellcasting ability modifier is
+0 for the item, and your proficiency bonus does apply.
This passage directly refers to the Thief feature we are looking at, so provides rules if a DM decides to apply the ability check requirement to the Thief trying to use the spell scroll.
This now opens the question of whether the proficiency bonus applies to an ability check, instead of just to cases where the spellcasting ability bonus is required (like when making an attack roll with the spell).
So, what does it mean for someone to be proficient?
- Choose a class (PHB 11)
Your proficiencies define many of the things your character can do
particularly well, from using certain weapons to tell a convincing
lie.
The passage from DMG 141 about the Use Magic Device feature explicitly says that the proficiency bonus applies to making spellcasting ability checks for the Thief when using a magic item, which means that passage is saying that a Thief can use a magic item particularly well.
This means that the proficiency bonus should apply to the ability check to attempt to use the scroll. To argue otherwise is to say that a Thief both cannot use a spell scroll particularly well, and can use it particularly well if they succeed in casting a spell from a scroll that uses an attack roll. That's seems like a bit of a contradiction.
Reliable Talent makes most spell scroll attempts succeed
If a DM gets pushback from their Thief player that requiring an ability check makes it hard to make good use of spell scrolls, the DM should point out that the Thief also has the Reliable Talent class feature by the time they get Use Magic Device.
Reliable Talent (PHB 96)
By 11th level, you have refined your chosen skills until they approach
perfection. Whenever you make an ability check that lets you add your
proficiency bonus, you can treat a d20 roll of 9 or lower as a 10.
As the DC is 10 plus the spell level, and that by level 13 a Rogue cannot roll less than a 15 on a check that allows adding their proficiency bonus, then the Thief will always succeed on spell scrolls up to level 5.
Summary
By strict RAW (both rules and rulings) a Thief can use spell scrolls, and there is nothing that requires a Thief to make an ability check.
A DM could reasonably require a skill check, and if so, the Thief can use its proficiency bonus as the only value it adds to the roll and keep in mind Reliable Talent applies.