Yes, You May
According to this page from Invest-faq
It is perfectly legal for non-resident aliens to trade equities on exchanges in the United States using US brokerage houses directly. (A “non-resident alien” (NRA) is the US government’s name for a citizen of a country other than the US who also lives outside the US.)
Of course there are certain formalities concerning tax treatment of such accounts, and these formalities must be clarified with the brokerage house when the account is opened. Individuals who are not US citizens must complete a W-8 form, which is a certificate of foreign status, and return it to the brokerage house.
The specific rules of how these accounts are taxed are described in IRS Publication 515 (Withholding of tax on non-resident aliens) and IRS Publication 901 (Tax treaties). The tax treaty is especially important. If the individual’s country of residence has an agreement (tax treaty) with the US government, those rules apply.
The relevant Investopedia page says:
There is no citizenship requirement for owning stocks of American companies. While U.S. investment securities are regulated by U.S. law, there are no specific provisions that forbid individuals who are not citizens of the U.S. from participating in the U.S. stock market. However, even if a non-U.S. citizen can legally trade U.S. stocks and bonds, it may still be required (in addition to being advisable) for them to consult with an investment firm and use the services of a professional.
One of the goals of the Patriot Act of 2001, passed following the 9/11 terrorist attacks, was to prevent individuals with any links to terrorist activities from funding their illegal activities through the American capital markets. The act led to brokerage firms implementing more stringent requirements for verifying customer identities, particularly for non-U.S. citizens. Part of this legislation also requires stockbrokers to report any suspicious account activity to the U.S. government. However, these regulations obviously do not impact the majority of international investors because the vast majority of investors do not have any criminal associations.
Some brokerage firms may require non-U.S. citizens to produce additional types of identification documents in order to comply with their individual policies. This can include visa information, a valid Social Security number, or a Certificate of Status of Beneficial Owner for United States Tax Withholding and Reporting form (also called a W-8BEN). Some brokerages may also require non-U.S. citizens to submit paper applications versus submitting online applications to open accounts.
The Forbes article: "If You Trade Around The World, You Need To Know IRS Rules" says:
Non-resident aliens are subject to tax withholding on dividends, certain interest income and sales of master limited partnerships like energy companies. They have U.S. source income — effectively connected income (ECI) — on real property and regular business operations located in the U.S.
A non-resident alien living abroad can open a U.S.-based forex or futures trading account and not owe any capital gains taxes in the U.S. U.S. tax law has long encouraged foreign taxpayers to invest and trade in U.S. financial markets ... A non-resident alien living abroad can also open a U.S.-based securities account, but there could be some dividend tax withholding. If the non-resident spends more than 183 days in the U.S., he owes taxes on net U.S. source capital gains, even though he may not trigger U.S. residency under the substantial presence test.
Thus having a visa of any kind is not required. Anyone anywhere in the world who is not associated with terrorism may trade on US exchanges provided they comply with the appropriate tax, identification, and other laws of the US in doing so.