Upvote:1
Yes, you can. I am assuming there is any cruise line which offers this itinery.
On the question of visas for staying on board or disembarking:
If you want to disembark, then of course you need a proper visa for the US. If you can produce one, I guess you will not have any issues.
The more interesting problem goes the other way round: Let's assume you are visiting a harbor where you don't have a visa and therefore you would not be allowed to disembark. Some cruise lines make their own rules there ("better be safe than sorry") and won't let you even embark on some itineries if you fail to present a proper passport with visa for the ports visited. So I would double-check with the cruise line.
For example, many US cruise lines require EU cititzens to carry a passport even if only harbors within the EU are on the itinery, so a national ID card would be suffcient.