Backup

If your contacts are in iCloud or in any other email account then they are not backed up. Sign onto the account in a browser and export them.

Of your contacts are only on your phone then make sure you have twice the amount of space in your iCloud plan as the phone memory. Eg 16GB iphone 6 needs the 50Gb plan

I'll take a guess that you want your contacts restored from iCloud, not backed up to iCloud.

so

Settings, [your name], iCloud

turn on Contacts (green)