When a foreign entrepreneur wants to run their own firm in the US, they apply for the nonimmigrant E-2 Investor Visa. There are two ways to do this: either to launch a new firm or to acquire an existing one (certain restrictions apply; check with your immigration attorney prior to establishing or purchasing an existing business).
Although there is no “minimum” investment amount, the investment must be “substantial” and not “marginal” in nature. The immigration adjudicator must be persuaded that your investment is enough to run the proposed endeavor.
The ability to demonstrate that the investor’s role is to “grow and direct” the firm in the United States is one of the essential components of a successful E-2 application. If there are communication difficulties, a manager who will oversee daily activities must be hired.