The odd thing is you cannot do this on an Android device. I tried to purchase more Drive storage via the Drive app on my Nexus 5X and it kicks me out the browser and opens the same Drive upgrade page as using a browser on the desktop. Clearly this is a move to get iOS users to start using Drive on their devices, saving $5 or getting 2 months free is a good start in my opinion. This is an IAP on iOS and the money comes from your Apple account so buy an iTunes Gift Card and start using more storage on Google Drive.
To access the upgrade in Drive:
- Tap the settings gear on the lower left of Drive (next to your email address)
- Tap Storage
- Upgrade Your Storage