Yes. There is no prohibition against non-U.S. citizens forming a corporation or LLC unless you or your country is outlawed by the US Department of the Treasury on its OFAC list (Office of Foreign Asset Control). Business entities owned by non-US citizens must register with the US on the one page FBAR form if over $10,000 is connected to the company. All entities other than single-member LLCs without income substantially connected to the United States must report LLC income to the IRS.
Businesses operating outside the US by non-US citizens may need an Apostille or document legalization for transactions or government compliance in their home country. If the country in which the company operates has signed the Hague convention, an Apostille is appropriate. Otherwise, the LLC will need document legalization certifications with which IncNow can assist in obtaining.