The latest update (2.16.15 on iOS) lets you send GIFs. This works even if your friend has the Android app: they just won't be able to reply with another GIF.
To send a GIF, press the + icon, then Photo & Video LIbrary. You can select any video up to 6 seconds long, and you can also 3D Touch on a Live photo from your Camera Roll, swipe up and select Send as GIF.
You can even copy and paste a GIF from Giphy (which has a massive searchable library) if you also install the GIPHY Keys app from the Apple App Store. Once done, go to Settings > General > Keyboard and add a new keyboard. You'll see GIPHY Keys in the list. Select it, then tap on it and enable Allow Full Access.
When you're back in WhatsApp, switch to the other keyboard by pressing the world symbol, then search for your GIF. Tap on one to copy it, and paste it into the message.