The short answer is "NO". As a foreign student under F-1 status, you must not work without permission, whether it is for an employer or for yourself as an independent contractor. Doing so will invalidate your F-1 status and render you out of status. Many people incorrectly believe that because they are not technically working for any employer, and that they are simply working for themselves by doing gigs here and there for companies such as Uber, Lyft, or Doordash, etc., such work would not trigger a violation of the immigration law. Even driving Uber for one trip is sufficient to trigger a violation of your F-1 status.
So before you decide to engage in any activity for pay, you should first consult with your school's Designated School Official (DSO). You may also contact us for a consultation regarding your situation before you do anything.