Board Thread:Questions and Answers/@comment-5693502-20140410203934/@comment-1268838-20140413203329

Well, Hollows are technically Souls themselves - they just don't have hearts. Asides from that, Uryuu insinuated that Arrancar have anatomy similar to that of Shinigami, hence why he was able to seal away Cirucci's spiritual power. On top of that, Byakuya stated that Zommari's ability was similar to Kidou, which doesn't necessarily mean anything, but it might be applicable to all Arrancar abilities, for all we know.

All that aside, while I do think it is certainly possible for an Arrancar to learn Kidou, it's very unlikely. Sure, they can manipulate their spiritual power just fine. But they would need someone to learn it from - all Shinigami with few exceptions have to study at the Academy for 6 years to learn that stuff.