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.
From the "Your Spellbook" sidebar, page 32 of the Player's Basic Rules (v0.2):
When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.
Emphasis mine. Only spells on the Wizard list can be learned in this way. In this area, there is no difference between spells written in a spellbook and spells written on scrolls. The difference is between Wizard spells and non-Wizard spells.
Even if the game allowed you to copy a non-Wizard spell into your spellbook, we have in Preparing and Casting Spells, page 30:
You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell).
So even if you could write non-Wizard spells in your spellbook, you couldn't prepare them and therefore couldn't cast them.
Further down the same page, you can cast rituals without preparing them, but even there, we have:
You can cast a wizard spell as a ritual if that spell has the ritual tag and you have the spell in your spellbook.
So, you can't copy non-Wizard spells into your spellbook, and even if you could, there's just no way to cast them.
Wizards can't use scrolls that are not on their list either, since we have on page 60 of the DM's Basic Rules:
If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible.
As to why this is (from a narrative perspective), every method of spellcasting works differently. For example, the Wizard and the Sorcerer probably have the most similar spell lists, but the Wizard uses magic through painstaking study and preparation, where a sorcerer simply unleashes the power they have within them. So a spell that isn't on the Wizard spell list is probably just impossible to cast using the Wizard method of spellcasting.
From a balance perspective, obviously it would be completely unfair if Wizards had access to every spell in the game.
Best Answer
He learns primarily from leveling up, but not only that way.
As I emphasized on this quote, the sorcerer can learn any spell from the sorcerer/wizard spell list. When learning these spells, he learns them spontaneously when he concentrates on his spells the first time after leveling up. Most times, the spell will just pop-up on the sorcerer's mind this way.
The other method, the study, is to allow sorcerer players to research and learn spells developed by themselves or others; spells that aren't on the book. Basically, originals or spells from a source that the DM doesn't use but allowed a PC/NPC to research that specific spell.
If your spell is on the sorcerer/wizard spell list from a sourcebook that your DM allows and he didn't forbid that specific spell, you just level up and learn the spell with no further effort from your character.