We present TouchWalker, a real-time system for controlling fullbody avatar locomotion using finger-walking gestures on a touchscreen. The system comprises two main components: TouchWalker-MotionNet, a neural motion generator that synthesizes full-body avatar motion on a per-frame basis from temporally sparse twofinger input, and TouchWalker-UI, a compact touch interface that interprets user touch input to avatar-relative foot positions. Unlike prior systems that rely on symbolic gesture triggers or predefined motion sequences, TouchWalker uses its neural component to generate continuous, context-aware full-body motion on a per-frame basis-including airborne phases such as running, even without input during mid-air steps-enabling more expressive and immediate interaction. To ensure accurate alignment between finger contacts and avatar motion, it employs a MoE-GRU architecture with a dedicated foot-alignment loss. We evaluate TouchWalker in a user study comparing it to a virtual joystick baseline with predefined motion across diverse locomotion tasks. Results show that TouchWalker improves users' sense of embodiment, enjoyment, and immersion.