As you might expect, the specific requirements to be eligible for a teaching assistantship vary from one university to the next, and from one department to the next. The only people who can answer your question are staff at each of the departments you're applying to. Ask them!!
To give one example: My public US R1 university has a strict requirement of a 24 or better on the speaking portion of the TOEFL, or an 8 or better on the speaking portion of the IELTS, in order to be a teaching assistant. Minimum TOEFL/IELTS requirements for admission without a teaching assistantship are somewhat lower; however, many PhD programs (like mine) have a TA requirement, and so the requirements for TAships are also de facto requirements for admission into those programs. Some graduate programs have higher TOEFL/IELTS requirements than the campus-wide minimum, and some graduate programs also assess English proficiency independently through interviews, writing samples, and the like.
Of course, meeting a department's English-proficiency requirements for a teaching assistantship does not guarantee that that department will offer you a teaching assistantship. It just means that you're eligible.