The rapid advancement of digital technologies and artificial intelligence has fundamentally transformed the nature of contemporary conflict, enabling influence operations that target human cognition as a strategic domain of hostilities. This article examines how international law, particularly the Law of Armed Conflict (LOAC), should regulate AI-driven algorithmic influence operations that function as instruments of cognitive warfare within hybrid conflicts. Employing a doctrinal legal research method, this study undertakes a normative and analytical examination of existing international legal principles, complemented by critical evaluation of emerging scholarly debates and policy developments. The findings demonstrate that current LOAC frameworks are structurally designed for kinetic warfare and are therefore ill-equipped to capture the legal relevance of algorithmic influence, resulting in significant gaps concerning attribution, civilian protection, and sovereignty. The analysis further reveals that existing jus ad bellum and jus in bello doctrines fail to adequately regulate non-kinetic cognitive harm and systematic narrative manipulation, allowing strategic exploitation below traditional conflict thresholds. The article formulates normative and institutional proposals for a revised legal framework grounded in cognitive protection, due diligence obligations, and enhanced corporate responsibility. It concludes that international law must evolve towards formally recognising cognitive warfare as a regulated domain of armed conflict to ensure the effective protection of cognitive autonomy, democratic stability, and international security.