Can You Play GTA 4 on PS Vita? No — Never Released

No. Grand Theft Auto IV was never released on PlayStation Vita.

Why

• Vita hardware cannot handle GTA IV's engine (designed for PS3/360/PC).
• No port exists on PlayStation Store.

Vita-Compatible GTA Games

• GTA: Liberty City Stories (PSP, playable on Vita via backward compatibility)
• GTA: Vice City Stories (PSP, playable on Vita)

To Play GTA IV

You need a PS3, Xbox 360, or PC (even modest modern PCs run it well).