Only If Sources Beyond the Player's Handbook Are Used
Omitted from the online sorcerer description is the following from the Player's Handbook:
[The sorcerer's] new spells can be common spells chosen from the sorcerer/wizard spell list (page 192), or they can be unusual spells that the sorcerer has gained some understanding of by study. For example, a sorcerer with a scroll or spellbook detailing an unusual sorcerer/wizard spell (one not on the sorcerer/wizard spell list in this book) could select that spell as one of his new spells for attaining a new level, provided that it is of the right spell level. (54)
Emphasis mine. Using a very hard reading of the rules as written, if the DM determines the sorcerer can gain "some understanding of [the spell cure light wounds [conj] (PH 215-6)] by study" from the scroll and the spell cure light wounds appears on the Sor/Wiz spell list in another source other than the PH, the sorcerer can add it to his spells known.
As the above is largely campaign-dependent, it needn't be a scroll. The DM determines what exactly the sorcerer can study to gain this understanding (e.g. ancient dragon scales possessing the secrets of weird magic, the corpses of magical minions, the drippings of sacred candles).
I am, however, unfamiliar with a published setting or source that adds cure spells specifically and directly to the Sor/Wiz spell list.
However, another source can totally be the DM's campaign notes. Thus, in a campaign that amends the Sor/Wiz spell list, the sorcerer could, upon understanding the spell via study, select that spell as a new spell when he reaches the next level if the spell's on the Sor/Wiz list at the appropriate level.
The DM should look askance at a player who claims his authorship of another source on a cocktail napkin amends his character's spell list, unless the source is accompanied by an appropriate bribe.
Yes; the ruling is now official and explicit from Sage Advice
As Dale M's previously-accepted answer said, the PHB rules for the Arcane Trickster imply that its class spell list is the Wizard's spell list.
This was made explicit in the official Sage Advice, which says:
For you to meet a spell scroll’s requirement, the spell on the scroll needs to be on whatever spell list is used by your class. Here are two examples. If you’re a cleric, the spell must be on the cleric spell list, and if you’re a fighter with the Eldritch Knight archetype, the spell must be on the wizard spell list, because that is the spell list used by your class.
From the example of a Eldritch Knight, we know that there is no class list of spells for the fighter class, but the class list for a fighter that becomes an Eldritch Knight is the wizard class list. We can conclude that there is no class spell list for rogues, but a rogue that becomes an Arcane Trickster has the wizard spell list, "because that is the spell list used by your class."
Thus an Arcane Trickster can use spell scrolls of spells that are on the Wizard spell list.
Thanks to InternetHobo who encouraged Rubiksmoose to cite the SA Compendium in their answer.
Best Answer
This can work.
Wizards don't learn spells; they copy them to their spellbooks and prepare them. But besides this small detail, your scenario would work, if the following criteria are met. (This answer assumes that the optional rules for Scribing a Spell Scroll from Xanathar's Guide to Everything will be followed.)
Sources:
Addendum: Ryan C. Thompson points out that in lieu of the Scribing a Spell Scroll rules from Xanathar's Guide to Everything, the Crafting a Magic Item rules from the Dungeon Master's Guide could also be used to create a spell scroll. Those rules would replace my points 3 through 5 above. Both sets of rules are optional and subject to DM allowance.