If you are authorized to work in the US on a professional visa, AND the CC does not require ( via check or bullet ) you to certify that you are a citizen then of course. Never ever intentionally lie on credit applications. Permanent residents are not citizens but can get any credit card they qualify for.

You should NOT apply for business cards. Not illegal but the nature of your visa requires you to work for a specific sponsor or employer. Those stupid points can come back to haunt you if you decide to proceed to a permanent residency petition. Not worth it.

Come to think of it, most H1Bs will apply for permanent residency and it is necessary to maintain a clean record. A bankruptcy or an arrest before becoming a permanent resident is a big red flag that will cause problems.