The short answer is "it depends". Corporations are required to be owned by citizens or resident aliens.
This is because an owner must reside in the jurisdiction, or have a physical presence, in order to be incorporated. This is to ensure that the business is invested in the community for tax purposes. Although foreign persons can be shareholders of a C Corporation, unfortunately, they cannot be an owner of an S Corporation.
Many states designate that an LLC can be owned by anyone, including a non-US resident. This means that a person not residing in the jurisdiction can incorporate as an LLC and operate it within US tax codes without actually living here. There are, however — depending on the state — certain restrictions that must be followed.
If the field in which an LLC is operating requires licensure in a state, then those guidelines must be followed to legitimately operate in the US. Furthermore, applying for a federal employee identification number (FEIN) requires that one of the owners has a taxpayer identification number, which is restricted to citizens of the US and foreign-born persons legally entitled to work here. So, all in all, foreign persons may need to partner with a US citizen to effectively operate an LLC in the US.
In the case that a person qualifies as a "resident alien" under tax codes, they can be part of both Corporations and LLCs, as owners, operators or shareholders. A resident alien is defined as one who meets either the green card test or the substantial presence test for the calendar year.
Incfile is certainly up to speed on foreign qualifications for incorporating as an LLC. We can help by becoming the company's Registered Agent and by providing legitimate documentation through our Corporate/LLC Kit. Both of these services ensure you are current on tax requirements, withholding needs, and can represent in a formal fashion. The Kit in particular provides a seal that can be applied to documents needing credibility attached.