Go to icloud.com and sign in. (You can do this on mobile too.) then tap on account settings then go all the way down and tap on restore contacts. This will allow you to use a iCloud backup and take the contacts off of it. Note that if your iCloud is full you won't be able to back up so there will be no back ups to restore. also note that backups are done automatically. Also note that if your last backup was during the contact you want was deleted, don't worry! All your previous backups are never deleted unless you do it manually.
If you want to learn more about back ups check out this article: How to back up your iPhone, iPad, and iPod touch with iCloud - Apple Support, and this one: Restore contacts, calendars, bookmarks, and more using iCloud.com - Apple Support