It depends on residency status, treaty elections, and whether the work is considered US-source income. F-1 and J-1 students are usually classified as nonresident aliens for generally up to their first five calendar years, because the substantial presence test does not count their student days. During this time, they file Form 1040-NR.
As nonresident aliens, these students are generally exempt from Social Security and Medicare taxes on authorized employment. However, federal income tax is usually still withheld from paychecks by default. This income tax withholding applies unless a specific tax treaty reduces or eliminates the obligation.
Over time, a student's status can flip to resident alien, which changes the tax rules and requires filing a standard Form 1040. Because employers often withhold federal taxes by default, the payroll deductions might not match the correct tax position. It is important to have the facts reviewed to ensure accurate compliance. Consider exploring professional US expat tax returns preparation before assuming zero US tax liability.