No. You report as wages, but you do not pay Self-Employment tax. According to the IRS:
Green Card Holders (Lawful Permanent Resident)
If you are a green card holder working for a foreign government or
international organization, you generally must report your earnings as
wages but are not subject to self-employment taxes on those earnings and
may not voluntarily pay self-employment tax on those earnings.
[Edited 04-09-2019]
