Is it possible to assign a static IP address without a DNS? Is it possible to assign a static IP address without a DNS in Android 5.1? Is there anyway to achieve it? I can do this in iOS so I'm wondering.
First, without DNS the network connection won't be much helpful to you: you will need DNS to resolve host names to IPs – or entering something like www.google.com into the browser's address bar will just give you an error.

Which does not mean you cannot use a DNS server other than Google's.

From your homescreen:


Press the Menu key, select Settings
Go to your WiFi settings, where your list of known/available networks is displayed
Long-Tap (tap-and-hold) the entry for your AP
Select Edit
Tap Advanced


Now you will see a form allowing you to override things: you can disable DHCP, then specify a fixed IP plus the related network settings – mask, default route, and – Tada! – DNS servers.