It doesn't say it sets things on fire like fireball or burning hands so no, it does not.
If I were the GM, yes it would
(1)Web states that " fire can set the webs alight..."
(2) Scorching ray:
Of course your GM may interpret it differently, and that is all that really matters.
We are told the following about being set on fire: "Characters exposed to burning oil, bonfires, and non-instantaneous magic fires might find their clothes, hair, or equipment on fire. Spells with an instantaneous duration don't normally set a character on fire, since the heat and flame from these come and go in a flash." -- this applies to characters and not everything in general, but seeing as there is no general guidance anywhere extrapolating from it is not unreasonable.
Scorching ray is an instantaneous duration spell with the fire descriptor. The spell description does not mention anything specific about setting things on fire. The fire descriptor does not have any specific rules attached to it about setting things on fire.
However, web says that "The strands of a web spell are flammable. A flaming weapon can slash them away as easily as a hand brushes away cobwebs. Any fire can set the webs alight and burn away one 5-foot square in 1 round."
I would personally qualify scorching ray as "any fire" (the description says "You blast your enemies with a searing beam of fire." if the fire descriptor wasn't enough of a clue), and thus it would indeed set the web on fire. The original quote about instantaneous fire not working is trumped in my opinion by "specific trumps general" (if you even rule it applies to begin with since the web is not a character).
My argument to Atzen's point would be that a flaming weapon doesn't set things on fire either, but web states that it can slash through them easily. So obviously, it is not just things that can actually set something on fire that only work on web.
Now, someone can counter with the argument that web, as written, actually has two conditions. There is general condition that states that any actual fire applied to the webs can clear them away, which would imply things that provide non-instantaneous fire damage. Then there is also very specific exception for only a flaming weapon, though a flaming weapon cannot normally set things on fire (though the fluff says that the weapon is coated in a sheath of flame, or whatever).
So, you already see that there is interpretation involved and you aren't going to get a "right answer". The only answer that matters is your GMs.
I would still lean very heavily on the *ANY* in "Any fire can set the web alight" and scorching ray's fluff stating it is a "beam of fire". But that is just me...
Count me in with the group that says scorching ray counts as fire for the purposes of "Any fire can set the web alight".