No, not directly. The PS2 controller port is proprietary (PS/2-style 9-pin); Xbox controllers use USB (original Xbox) or proprietary wireless (360/One). The PS2 cannot enumerate USB HID devices as controllers.
Buy a DualShock 2 ($10–$15 used) or a modern controller + Brook Wingman SD ($60) for wireless on real hardware. For PC, just use PCSX2.