This is a seven-piece endgame so you can always ask a tablebase. This position is a tablebase draw.
The first thing to note is that if Black trades their Rook for your pawn, then you can't really win. Your opponent's pawns are too advanced, and your King too far away. But you won't lose either, because you can always keep checking them with your Rook from behind, until they put their King on the h-file (whereupon you play Rf8, preventing the f-pawn from promoting) or on the f-file (whereupon you play Rh8 with the same idea).
This is the basic defensive idea:
[FEN "8/P1R5/1K6/7p/5pk1/8/8/r7 w - - 0 1"]
1. Rc5 {More about this move later.} Rxa7 2. Kxa7 f3 3. Rc8 {Standard is to go to the end of the board, since this maximizes the distance the King has to move to stop a frontal check.} f2 4. Rf8 Kg3 5. Rg8+ Kh2 6. Rf8 {Preventing the f-pawn from advancing.} Kg2 {Black obviously cannot allow Rxf2, so the King must return to the g-file.} 7. Rg8+ Kh2 8. Rf8 {Black has made no progress.} Kg2 9. Rg8+ Kf1 10. Rh8 {Neither Black pawn can advance.} Ke2 11. Re8+ Kd2 12. Rf8 {Black will have to agree to a draw sooner or later.}
Since you can't win, the question is: can you induce an inexperienced opponent to make a mistake? You can try, that's why the above line starts with 1. Rc5. If opponent doesn't realize you are threatening Ra5, then they might throw out 1...h4?? and lose. Another cheapo* you can try is, at the end of the above line, play 12. Rd8+. A careless player might think "it's just another check", play 12...Kc2?? and lose after 13. Rf8 (the King can't get back in time to protect the f-pawn).
*"Cheapo" is chess terminology for a cheap (i.e., not very sophisticated) trap.
