On my iPhone, I just noticed that if I do a Google Search (in Mobile Safari) and select a result on quora.com, the result page launches the native Quora app on my phone.
I'm reposting an answer to my own related (but was originally Ruby-on-Rails-specific) question from here: Rails: redirect_to 'myapp://' to call iOS app from mobile safari
You can redirect using javascript window.location.