PS1 Game Where a Sword Wraps Around Your Hand at the End

That's Blood Omen: Legacy of Kain (1996, Crystal Dynamics / Silicon Knights).

In the final cutscene, the protagonist Kain claims the Soul Reaver—a cursed, sentient blade. The weapon's spectral coils wrap around his arm and fuse with his hand, binding him to its hunger for souls and setting up the entire Legacy of Kain saga.

It's an iconic moment that defines Kain's tragic transformation from murdered nobleman to vampiric anti-hero.