Qualifying for Arcane prestige class using Divine magic

[Inuzuka]

Without needing to change race or multiclass.

Is it possible?

[Baroncognito]

Yes. There is a feat: Scaled Disciple, for Kobolds. It allows a kobold to use spontaneous divine casting to meet prerequisites for Dragon Disciple and allows Dragon Disciple to advance divine spellcasting levels.

[A_S]

Ask your DM.

There are various things that might do it. The ones I can think of are:
The Southern Magician feat, from Races of Faerun. Lets you cast divine spells as arcane and vice versa. Has the annoying line "The actual source of the spell's power doesn't change" with no real explanation of what that means.
The Alternative Source Spell feat, from Dragon #325. This is probably the least ambiguous option, but Dragon Magazine is in a sort of nebulous official/3rd-party void, and isn't allowed at many tables.
The Geomancer prestige class. Whether this one works depends on whether "qualifying you for prestige class requirements" constitutes a "spellcasting parameter," a term used in the PrC's Spell Versatility feature and not clearly defined anywhere in the rules.
If you're a Ranger or a Paladin, the Sword of the Arcane Order feat from Champions of Valor, which lets you prepare and cast Wizard spells from a Wizard's spellbook out of your Ranger or Paladin slots. These spells smell a whole lot like arcane spells, but they're not explicitly stated to be so in the feat description.
If you don't need a specific level of arcane spell, the Magical Training feat from Player's Guide to Faerun. It lets you cast level 0 arcane spells without blowing a class level on it. First level only feat, though.
None of these options are RAW-airtight, and they're the kinds of things that get argued about on these boards over and over again. There's really no better answer than "ask your DM."

*edit* I was assuming 3.5; if you're playing PF, then I'll leave it to more knowledgeable others to answer.

[Nettlekid]

I've been unsure, but does (Greater) Anyspell from the Spell domain cut it? Throughout the spell description it says Arcane spell, not Sorc/Wiz spell as a Divine spell or anything like that. If so, then any character with access to that spell (via domain or as an Archivist or whatever) is capable of casting Arcane spells.