Can I add Brave as search engine for safari on iPhone

Brave does not offer a standalone search engine. It's incorporated in their app.

Get the app here: https://apps.apple.com/us/app/brave-private-web-browser-vpn/id1052879175

No. You would need to install the Brave browser on your iPhone (or some other browser that supports the Brave search engine, if there is one).

I think they may for some browsers other than their own based on https://search.brave.com/help/default