Can I call myself an assistant professor without a PhD? I've recently gotten a job as lecturer and economics course module developer at a new university this fall. The position is intended as permanent. There is opportunity for funded research but that isn't an objective of the chairs due to the newness of the university. 

What is strange is that the position is called "Assistant Professor" which  makes no sense due to the size of the institution and the lack of research required by it (It is a private university).

I am currently enrolled in a PhD program but have some time to defend my thesis. I'm wondering if it's fair to call myself an "assistant professor" or not being that I haven't been endowed with my PhD yet.
the position is called "Assistant Professor"


If you hold an appointment as an assistant professor, then you are an assistant professor. Still, I understand your concern....


  kinda makes no sense due to the size of the institution and the lack of research required by it...however this is a bit of a no-name brand institution


Context is everything. 


I agree it would look foolish or pompous if you use your title in a way that gives the impression you are a professor at an R1. When meeting colleagues at different institutions, you may wish to describe yourself as a lecturer or say "my title is assistant professor, but it's mostly teaching" or something unambiguous like that. 
On the other hand, everyone at your home institution should understand what an "assistant professorship" at that institution entails, so there is no issue with you using the title internally.
Similarly, non-academics don't know or care about the subtle differences in academic rank, "I'm an assistant professor" is fine in such contexts. 


Regardless, your PhD (or lack thereof) is irrelevant.

Sadly, such overloaded terms in commonplace in Anglophone academia. Many of us with doctorates select the salutation "Mr./Ms." to avoid being confused for an M.D. ("real doctor"). Those with PhDs from online schools face a similar dilemma.