Android - How to set HTTP proxy and proxy authentication credentials in wifi?
According to this, you need an external app and you need to root the phone.
Some other solutions shared in a Google Code issue thread.
Using Gesture Search, I entered "proxy" and got to the Proxy settings on my Droid. Don't know how to get there otherwise, and don't know if it actually works, but there you go. (Someone else mentioned it in that Google thread.)
To modify the proxy settings in Android 4 and Samsung Galaxy you should do this:
Go to Settings / Wifi. Long-click on your network and select Modify network. Scroll down to Show advanced options which should show you the proxy options.
My Samsung Galaxy S II has proxy settings enabled under
Settings > Wireless & Network > Wifi settings > Advanced
I can set a proxy address and a port number.
The proxy I'm sitting behind requires authentication tho and I'm having trouble finding these settings.