Hi Doc,
Welcome!
I'm just curious: What's the reason for your interest in an "officer position"?
On most cruise lines there are different definitions of an "Officer".
Most commonly, an Officer is either an MTO Officer (Marine and Technical Operations - Engine/Deck, which mostly requires formal Marine Engineering or Navigation/Deck degree and STCW license) or is part of Senior Management - Hotel Director, HR Manager, Cruise Director, etc.
Other positions have similar privileges as MTO Officers but mostly fall under either Hotel or Entertainment department (and HR where available), those positions, if not Department Heads are what is referred to in maritime terminology as "Petty Officers", that is, they have a (usually) white uniform but have no marine license or responsibilities with regards to Ship Operation (except for Safety Duties). Some will refer to those positions as "Staff positions" and may include vendors (usually Merchandise, Spa, Medical and Photo departments).
Since your profile says you are from the US, depending on your background, my advice for you would be to apply for a position in HR. Due to the role and certain (legal) responsibilities involved, US candidates will be preferred when considering senior positions in that department. As an added benefit, the "promotion ladder" is quite short - you are usually one or two steps removed from being (becoming) an HR Manager - usually part of Steering Committee and/or Senior Management.
If you search around the web and look at cruise line company websites, you will usually find that there is a separate recruitment section/contact for US citizens.
Good luck.