I really want to submit to viXra to stake my claim on the paper's idea. I don't want to submit it to arXiv. I searched PRA's policy on this without much success. I have read the following documents, yet I can't figure out what is their stand on the issue.
Physical Review is unlikely to notice or care what you post on viXra, or nearly anywhere else, so long as you hold the copyright and your work has not been accepted by a journal.
For opinions on viXra, see What are the differences between viXra.org and arXiv.org?.