Problem in signing up to facetime

See If you get an error when trying to activate iMessage or FaceTime https://support.apple.com/en-us/HT201422. 

Use these support options if you need more help.

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple ID account security for country-specific and region-specific help

 https://support.apple.com/en-us/HT204169

FaceTime should work on WiFi. It works on my iPad that has no cellular capability.

Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.      

You are welcome. Glad to help.