This paper presents a socio-technical framework for measuring organizational capacity for cyberinfrastructure (CI) implementation, adoption, and diffusion at the team's level. CI implementation is an example of big data science project in data-intensive projects funded by the US National Science Foundation (NSF), providing a unique case for understanding big data science teams from an important field that is academic and scientific in nature. We argue that organizational capacity can be defined by the three dimensions of foundational technical expertise, daily social interactions, and enduring organizational qualities. We provide scale items for measuring these three dimensions, using a questionnaire in a self-reported and self-reflexive fashion. The overall average score and the individual composite scores of the three dimensions (and their sub-dimensions) can be used as feedback and capacity building activities as intervention strategies. Future research will statistically validate the framework using exploratory and confirmatory factor analyses.