The Nintendo DSi and DSi XL only support WEP encryption. They cannot connect to WPA or WPA2 networks natively.
Use a smartphone, laptop, or travel router to create a WEP-secured hotspot bridged from your main WPA network. Connect the DSi to this hotspot.
Downgrade your main router's security to WEP. This exposes your entire network to trivial cracking. Strongly discouraged.
Some homebrew-compatible adapters (e.g., certain R4i/RTS cards with Wi-Fi) claim WPA support via custom firmware, but these are unofficial, complex, and may violate terms of service.
Upgrade to a Nintendo 3DS/2DS or Switch—both support modern WPA2/WPA3 security natively and play DS games via backward compatibility.