Q: Can you suggest a journal with rapid turnaround time for a study on academic integrity?

Academic integrity sounds like an interesting topic to write about, but it might be difficult to tell you exactly which journal might be best suited for you without knowing more about your study, especially if it is focused on a specific discipline, e.g., research on academic integrity in the field of biomedicine. Further, it would be better to understand what you mean by rapid - in some fields, a  period of of 2-3 months from submission to acceptance is considered rapid. But the good news is that academic integrity is a topic of interest that has applicability across all scientific disciplines and you might have a range of journals to consider. Also, choosing the open access route might give you more avenues to try out.

To begin with, you could take a look at some specialty journals that focus on scholarly publishing, e.g., European Science Editing (managed by the European Association of Science Editors), Learned Publishing (managed by the Association of Learned and Professional Society Providers), or Science Editor (managed by the Council of Science Editors). You could also check multidisciplinary journals such as PLOS ONE (the open access multidisciplinary journal that offers rapid publication), BMJ Open, or ScienceOpen (which also works on the post-publication peer review model). You could also consider querying the journals/publishers mentioned in this list. Remember to search the journal's//publisher's archives to check if they have published papers on similar topics.