World of Warcraft on Nintendo DSi: Absolutely Impossible

Absolutely not.

• Architecture: WoW (x86/ARM64 client) requires Windows/macOS/Linux/Android/iOS. DSi runs bare-metal ARM9/ARM7 firmware
• Resources: DSi: 16 MB RAM, 133/67 MHz CPUs. WoW Minimum: 2 GB RAM, 2+ GHz CPU, GPU w/ 512 MB VRAM
• Storage: DSi: 256 MB NAND. WoW: 100+ GB
• Input: No mouse/keyboard support. Touchscreen only
• Network: DSi supports 802.11b/g (WEP/WPA only). WoW requires TLS 1.2+, modern auth

Closest DS/DSi Experiences

• Phantasy Star Zero (DS) — Online Action RPG, 4-player co-op
• Dragon Quest IX (DS) — Online multiplayer, trading
• RuneScape — Mobile (Android/iOS) only; no DS client