Rioja can be both basque and castillian depending on what you take in consideration.
Basileios Makedon is somehow right, but not 100%. Let me explain. It is true that the first words in writen castillian appeared in Rioja, but so did the first words writen in basque (in the same text, in fact). Besides, castillian was not only born in Rioja, but it covered parts of northern Burgos (Las Merindades), part of Cantabria (Transmiera) and parts of westernmost Basque Country (Encartaciones and Valle de Valdegovia).
That being said, basque was spoken in Rioja until the XVII Century and Rioja has had a lot of relationship with basque lands since forever.
But, we don't have to fail in the misconception of equating language and culture.
So, to sum up, having Rioja as either basque or castillian would be correct. I guess, that to avoid political clashes and because it is hard to tell with a 100% precision what they felt back in the days, leaving them as castillians might be a smarter choice. Anyway, I won't tell what's more correct, just giving some info so people can have a better base of opinion.