Open the GIF in Safari, Messages, Mail, or another app
Press and hold the GIF
Tap Save Image or Add to Photos
Open the Photos app
Find the GIF in Recents or Animated
If needed, use the Files app to save the GIF first, then move it to Photos
If the GIF is in Messages, press and hold it, then tap Save
If the GIF is in Safari, press and hold the GIF, then tap Add to Photos or Save Image
If the GIF does not animate in Photos, make sure it was saved as a GIF file and not converted to a still image