You cannot directly transfer a PlayStation 2 video card to a desktop computer. Here is why:
Hardware Incompatibility
Different Form Factors: The PS2 uses a proprietary "Graphics Synthesizer" chip with a custom connector and bus system, not a standard expansion card.
Slot Mismatch: Desktop motherboards use PCIe (Peripheral Component Interconnect Express) slots, which are physically and electrically incompatible with PS2 hardware.
No Drivers: Even with a physical adapter, no software drivers exist to make PS2 graphics hardware function under Windows or Linux.
Better Alternatives
Upgrade Your GPU: Install a modern graphics card compatible with your motherboard's PCIe slot.
Use an Emulator: Play PS2 games on your PC via PCSX2. This requires a capable modern GPU for good performance but allows you to experience the library legally.
Bottom line: Fundamental differences in architecture make this transfer impossible.