Without commenting on possible reasons to move your Google contacts to iCloud and whether it’s worth doing so or not, the solution working for me was using iTunes.
Supposedly you can go to Google contacts, export all contacts as vCard, go to iCloud and drag and drop it to your address book. Unfortunately, that didn’t work for me. So far I’d say iCloud is flimsy at best, but that is a total different story.
1) Set up your iPhone to sync your contacts with Google.
2) Change your iTunes settings, so that you’re synchronizing these contacts with iTunes. It may
say this is unnecessary (and I’d normally agree), but just do it anyways.
3) Synchronize your iPhone with iTunes. (This step is the key to the success of this process.)
3) Disable Google contact sync on your phone. Just ignore a message saying that you’ll delete all contacts.
4) Set up iCloud and contact sync. It should now sync all your contacts with your address book.
The synchronization with iTunes can now be switched off again.
These simple step worked for me, but you never now. If you encounter any unexpected failures or have suggestions, please leave a comment.