Who can say? It's not like ZUN takes a census or anything.
Regardless, I think the answer is "quite large," particularly in Japan. The series is popular enough and well-known enough to support its own conventions and published works. There are musical groups such as IOSYS who can make albums solely based off of Touhou Project musical covers.
Here in the States, it's got more of a cult following, but it's nevertheless known enough on 4chan and other image boards like Danbooru. Seeing as how the games are not commercially distributed here, the fanbase is going to be relatively small...but still very large considering a complete lack of commercial distribution and advertising.