No, F-1 visa holders are not permitted to run or operate a business while in the U.S. unless the activity is part of authorized on-campus or practical training. Engaging in self-employment can violate visa conditions.

To stay in status, any work, whether online or in person, must be authorized by your Designated School Official (DSO) and tied to your academic program, like through CPT or OPT. Unauthorized work, including running a business, is considered a violation.

If you want to turn the business into a long-term opportunity, one option after graduation could be changing your status to a visa that allows entrepreneurship, such as an E-2 treaty investor visa (if you're eligible), or exploring sponsorship options that allow business activity.