If you're willing to take a few risks and have a good understanding of PSP hacking, you can install a custom firmware (CFW) on your PSP. This will allow you to run ISO files, including a free version of GTA: San Andreas.
Another option is to use an emulator on your PSP to play a PC version of GTA: San Andreas. This method requires a bit of technical know-how, but it's a viable option. how to play gta san andreas on psp free
While it's not possible to download the full game for free, Rockstar Games, the developer of GTA: San Andreas, has released a free demo version of the game for the PSP. The demo allows you to play a limited portion of the game, giving you a taste of what the full game has to offer. If you're willing to take a few risks