By RAW? No

The spellbook rules say this:

Once a wizard understands a new spell, she can record it into her spellbook.

It says "wizard" explicitly, so by a direct RAW reading of the rule, no. A Sorcerer can't do it.

It also says a wizard can copy into her spellbook, not into someone else's book. That makes sense, as it's hard for a wizard to decipher someone elses magical writing (and your spellbook is meant to be your writing).

A Wizard can add spells to their book from a scroll, so a Sorcerer with Scribe Scroll could create a scroll the Wizard could then use to put it in their book.

Your DM Could Allow It

All that said, if your DM wanted to allow it? It's not a big deal.

I'd probably allow it if a Sorcerer in my game wanted to do it. They still have to pay the cost to write into the book (100g per page of the spell), and it's not exactly giving the Wizard something they can't get elsewhere anyway.

Sometimes, getting hung up on the little details isn't worth the effort. IMO, this is likely one of those times.

How would you go about allowing it? Here's a few ideas on how it might work if your DM wanted to do it:

1. Have the Wizard do the writing, and let the Sorcerer act as the equivalent of another spellbook. You can use the existing rules on deciphering a spell (spellcraft check) for the Wizard to understand what the Sorcerer is saying, and if successful can copy the spell. (Thanks gatherer818!)
2. Have the Sorcerer just write it in the Wizard's book, then have the Wizard make a spellcraft check using the rules to decipher someone else's arcane writing in order to understand it. (Thanks G0BLiN!)
3. A Wizard can help another Wizard to learn a spell, in which case no check is required. You could houserule that a Sorcerer can also do that, in which case the Sorcerer could teach the Wizard, and the Wizard would do the writing into the book with no checks required. (Thanks Perkins!)

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.