Because a direct port doesn't exist, many players use custom homebrew mods that transform existing official PSP GTA titles into San Andreas look-alikes.
If your PSP runs official firmware (OFW), you cannot run homebrew. You need to install CFW. For modern PSPs, use Infinity 2.0 with PRO-C . This is reversible and safe. Once installed, you will see a new "Game" folder icon for homebrew.
Official support for San Andreas ended with consoles like the PS2 and PC because the PSP's hardware and limited disc space couldn't handle the massive state of San Andreas at the time. However, the community has found these alternatives:
To get started, your PSP must be running Custom Firmware. This is the essential first step that allows the handheld to run unsigned code and homebrew applications. Without CFW, the system will not recognize the modified game files. Once your system is prepared, you will need to find the specific "San Andreas for PSP" mod files online. These are typically distributed as ISO or CSO files.
Search for "GTA San Andreas PSP Homebrew Port" on reputable homebrew forums like Wololo.net or GBAtemp. Look for versions labeled "PSP San Andreas v1.0" or similar.