You can access a specific GIF on platforms like GIPHY and right-click on it. From the pop-up menu, click Save As to download it on your device.
Another method is installing a dedicated app on your smartphone to download the GIF. Simply head over to Apple App Store or Google Play Store to download apps like GIFwrapped(iOS) or GIF Keyboard(Android). These services will allow you to save the GIFs to your device instantly!