For those who want a stable, native experience, Rockstar released three official titles for the platform: Grand Theft Auto: Liberty City Stories Grand Theft Auto: Vice City Stories Grand Theft Auto: Chinatown Wars The Real GTA San Andreas for PSP!
Because a native port is impossible, the "PSP homebrew" scene created several workarounds to bring the San Andreas experience to the handheld: GTA: San Andreas Unity (PS Vita) gta san andreas psp homebrew