Nintendo DS Charger vs. DSi: Not Compatible

No. The original Nintendo DS (Phat) and DS Lite use a different barrel connector (slightly larger diameter) and voltage profile than the DSi and DSi XL. The DSi requires a dedicated DSi charger (or a multi-voltage charger with the correct tip).

Key Differences:

• DS / DS Lite: 5.2V / 450mA, 3.5mm OD / 1.35mm ID barrel plug.
• DSi / DSi XL / 3DS family: 4.6V / 900mA, 3.5mm OD / 1.0mm ID barrel plug (same as 3DS).

Forcing the wrong plug can damage the charging port. Buy a correct DSi/3DS charger—they're cheap and ubiquitous.