Royal Caribbean does not employ Priests, Ministers, Rabbis, or other religious holymen or women onboard their vessels but there is usually a Catholic Mass and/or other non-denominational service performed.
Many times Priests do cruise at a reduced rate in order to fulfill this passenger request. It is very common on Holland America and on Celebrity and I have seen it on most cruises that I have taken.
Just remember there is no guarantee, from the cruise line, that there will be a service on your cruise.
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It turns out they had a little 10-15 min. non-demoninational service (i.e. reading from a script) by one of the crew members -- she had never done it before and was very nervous. About 10 people showed up.
Yes, I've heard of ministers, pastors, rabbis, etc., volunteering to do the service, but have never heard that they were paid for it.