Being somewhere in the wide and diffuse field of complex-systems science, I am not aware of any generally accepted definition of complexity, let alone one that yields a measurable quantity. It’s more an “I know it when I see it” thing, and in my experience, there is common agreement that the term cannot and does not need to be defined rigorously (for reasons that I elaborate later).
I have many times witnessed that scientists dealing with more complex systems expressing a tongue-in-cheek superiority over those dealing with less complex but still complex systems, saying that they were not really complex.
In another example, the 90-page review paper The Structure and Function of Complex Networks applies the adjective complex to networks only a handful of times and not at all in a way that could serve as a definition.
If I were to define the field, I would say probably say something along the lines of:
Complex-systems science investigates phenomena that emerge from the (complex) interplay of perfectly or at least well understood components.
Thus, if you so wish, you can define a complex system as one that is principially capable of exhibiting such emergent phenomena.
Of course, these definitions inevitably inherit vagueness from terms such as emergence, well understood, or pricipially capable.
Moreover, once we understand a complex system, it becomes a well-understood component itself.
However, once we go down to specific research, these intricacies of the definition do not matter anymore:
As long as your research gains insights on phenomena that are not yet understood, it yields new knowledge – whether the system exhibiting the phenomenon is complex or not does not really matter in this respect.