Generally, a student on a F-1 visa cannot work for a company while in the US. They can take an active role, such as being a shareholder and possibly a board member. However, a student with a F-1 visa is unable to be a director such as a secretary because that is an active role with its day-to-day task.
As Dhara pointed out, the US government recently made an announcement that deals with F-1 visas. It’s worth pointing out that it only deals with a percentage of students on F-1 visas though. The government is allowing all STEM students (science, technology, engineering, math) on a F-1 visa the chance to work for three years following the “student” part of their visa.
If you need assistance figuring out your immigration rights then check out. Our collection of immigration / business attorneys have experience helping students on F-1 visas and would be happy to speak with you during a free consultation. Hope this helped!