Can you go on a cruise while on parole supervision? Will us customs stop and arrest you upon returning to the us?

Yes, Customs will stop you upon returning to the US. Best to have written permission prior to leaving the state. And should you somehow get this written permission be sure to carry this paper with you at all times when out of the state.

Ask your parole officer about this WAY ahead of the time you want to go on a cruise. If you decide to somehow "wing" it you're going to violate your parole and land back in the slammer pronto.