Which health insurance companies insure foreigners in the US?

If you are referring to private insurance, then contact an agent, this of course assumes you are legal. Also if the company you are employed with offers group insurance then you should qualify there as well.

If you are foreign visitor, seeking temporary health insurance during your stay abroad, you need Visitor Medical Insurance. Visitors Health Insurance is highly recommended for international visitors and foreign travelers visiting countries like the US and Canada, which covers the visitors health outside his or her home country. There are many plans from many visitor insurance providers, you can visit and then review the various options.