If I live and work outside the US but pay toward my student loan & interest "acquired in the US", do I file a tax return in the US to claim the interest paid?

The student loan deduction is a deduction which reduces your taxable income, and not a credit.

If you do not have taxable income, then there is no need to claim the student loan interest deduction.

If you are a US citizen/ resident then , yes you have to file a US return  and  can claim this interest  as an adjustment 9 if your AGI qualifies you.

If you are non-resident alien -- then , unless you have  US sourced / connected income  you do not file a US return and  this  loan-interest  is only pertinent for your country return