The government has commented:
“DHS carefully considered whether to allow volunteer positions to qualify under the STEM OPT extension program but has decided against permitting such arrangements. ... Requiring commensurate compensation for F-1 students – which does not include no compensation – protects both international and domestic students and ensures that the qualifying STEM positions are substantive opportunities. . . .”
You will need a Social Security Number ( https://www.ssa.gov/ssnumber/) in order to receive payment from your employer.
In general, as an F-1 student you will be exempt from Social Security (FICA) taxes for your first five years in the U.S., as long as you continue to declare nonresident status for tax purposes. Unless you qualify under a tax treaty between the U.S. and your home government, your earnings as an F-1 student will be subject to applicable federal, state and local taxes, and employers are required to withhold those taxes from your paychecks.
You may work on own, or use a local certified preparer, or web-based programs or software such as Glacier Tax Prep, or TurboTax. If you still need help or need information regarding taxes, consult the Internal Revenue Service.