The core rules say:
Beginning at 4th level, a ranger gains the ability to cast a small number of divine spells, which are drawn from the ranger spell list. A ranger must choose and prepare his spells in advance (see below).
To prepare or cast a spell, a ranger must have a Wisdom score equal to at least 10 + the spell level. The Difficulty Class for a saving throw against a ranger’s spell is 10 + the spell level + the ranger’s Wisdom modifier.
note that this is a little different from what the rules entry about spells says when it comes to other casters.
A bard casts arcane spells, which are drawn from the bard spell list.
A cleric casts divine spells, which are drawn from the cleric spell list.
The difference is that clerics obviously cast divine spells no matter what the spell is, a ranger however casts spells which are divine. the cleric rules imply that a cleric casting these spells makes them divine, the ranger rules do not imply that (at least in my reading), the spell itself is divine (and in the case of SotAO arcane). Even if you discard this, the rules say that they are drawn from the cleric/bard/ranger/x/y/z list. SotAO spells are from the wizard list, thus the rules must be expanded or maybe even adjusted...
Now with the SotAO feat a ranger obviously gets the ability to prepare wizard spells from a spellbook (with a reference to the rules about how wizards do that), which use intelligence as the key stat. The rules about preparing spells of either the arcane or divine type again are substantially different. The way a SotAO ranger prepares wizard spells is exactly the way a wizard prepares arcane spells and has nothing to do with how divine spellcasters prepare their spells.Conclusion...
Without the different way the rules about a ranger's spellcasting open up compared to other casters, and if you discard the matter about the part "from the ranger spell list" versus "wizard spells", the conclusion that SotAO spells are divine would be totally and indisputably RAW. If you argue that the rules are simply badly worded in the ranger's case and that the wizard spells are only an expansion to the rules, the case is clear: Rangers cast divine spells.
If you consider the way the spells are prepared and the rules text of SotAO, which explicitly mentions the connection to the arcane (even the name of the feat does imply this), you could argue that RAI it is totally intended that these spells are arcane.
If you also say that the ranger spellcasting rules do not explicitly say that all ranger spells cast are divine, and that the part about the "wizard spells" is a rules adjustment (and the fact that you do NOT get access to the wizard spell list which makes it even more awkward to rule this a rules expansion), you get to a "dwk/true dragon"-type of argument...