Here is the legal pathway:
If you want that —arcade handling, stunts, and combat—without legal issues, download these official PSP titles from the PlayStation Store (still accessible via PS3 or PS Vita store): Download Rumble Racing Psp
You cannot legally download Rumble Racing directly for PSP unless you rip your own PS2 disc and convert it. Most search results for "download Rumble Racing PSP" lead to abandonware or pirated content. Proceed with caution. Here is the legal pathway: If you want
file of the game, which can be loaded into the app's game list. Popular Racing Games Native to PSP and combat—without legal issues
A hybrid single-player + asynchronous multiplayer feature that leverages the original PSP’s ad-hoc spirit but modernized via cloud saves.