I do not think you should get a PhD from anywhere to be on law faculty in the US. You should do research about what higher degree(s) you obtain. For example, many (most?) of the faculty at law schools either have a legal degree (e.g., a JD) or are cross appointment faculty.
For example, I browsed the faculty at Yale, Michigan, and Texas Tech. The majority of faculty have JDs, with some have PhDs and JDs, and very few having only PhDs.
Edit: Upon further research I see that the American Bar Association views a J.D. as the same as a Ph.D.:
WHEREAS, the acquisition of a Doctor of Jurisprudence degree requires from 84
to 90 semester hours of post baccalaureate study and the Doctor of Philosophy
degree usually requires 60 semester hours of post baccalaureate study along with the writing of a dissertation, the two degrees shall be considered as equivalent
degrees for educational employment purposes;
THEREFORE, BE IT RESOLVED, that all appropriate persons be requested to
eliminate any policy, or practice, existing within their jurisdiction which
disparages legal education or promotes discriminatory employment practices
against J.D. degree-holders who hold academic appointment in education
institutions.
Based upon this new finding, I encourage you to see what US law professors have. Here are three ways you might find your answer:
- Find a US law professor and ask them if/how they would hire somebody with a similar background as you.
- Search faculty webpages until you find backgrounds similar to yours. Possibly even consider sending these people an email asking them for career advice.
- Ask your question on a US legal forum where more lawyers may be present. Possibly the Law exchange page. I think your question is on topic here, but sites like that would have more lawyers.