If you are a RESIDENT alien, then you are responsible for your own taxes and self-employment taxes just as a US Citizen would be. You are a resident alien if you pass either the green card test (ie. Lawful Permanent Resident) or the substantial presence test for the calendar year (January 1-December 31).
If this is the case and you are classified as a Resident Alien, then your client would have no duty to withhold tax for you as an independent contractor.
However, if you do not meet either the Green Card Test or the Substantial Presence Test, and you would be considered a Nonresident Alien, your client would be responsible for a tax withholding of 30%.
Click here for more information. https://www.irs.gov/publications/p515#en_US_2017_publink1000224965
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