Can a visitor in the US apply for a Green card?

A foreign national in the U.S. with a valid visitor's visa indeed may apply to adjust status to become a lawful permanent resident (to get a "Green Card") if he/she qualifies for such an application. Generally, eligibilities are based upon either a family relationship or upon sponsorship by a qualified employer for a qualified position for a qualified employee. If you may have a relative or an employer who is interested in sponsoring you for immigration benefits, then there really is no substitute for consulting with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.