If you file form 1040 (U.S. resident return), you must report, and are subject to taxation on your worldwide income. Non-Residents, who file form 1040NR, must only report their US sourced income. If you are a foreign national investing in the US, if your US visits make you a US tax resident for tax purposes, your worldwide income will become taxable.
For Form 1040, US citizens and GC holders have minimum filing requirements. As opposed to U.S. residents, non-residents do not have minimum income threshold for filing as long as they receive income from U.S. sources. On the same note, if you were a non-resident alien engaged in a trade or business in the United States, you must file even if you have no income from a trade or business conducted in the United States, or your income is exempt from U.S. tax under a tax treaty or any section of the Internal Revenue Code.