Can’t restore contact

iCloud: Restore contacts, calendars, and more in iCloud Settings

You can restore your contacts, calendars and reminders, or Safari bookmarks and reading list from an earlier version that was automatically archived in iCloud. For example, you might want to restore an earlier version of your contacts to recover some that were accidentally deleted.

When you restore an earlier version, your current version is first archived in iCloud so you can change your mind and go back to it.

Restore your contacts

You can restore your contacts and contact groups from an earlier version that was automatically archived in iCloud.

1. Go to Settings on iCloud.com, then click Restore Contacts (in the Advanced section).
2. Available versions are listed by the date and time they were archived.
3. To the right of the version you want to restore, click Restore.
4. There may be more versions than can be shown at once. Scroll to see more.
5. Note: Wait until iCloud finishes restoring your contacts before you change them. While it’s restoring them, any changes you make aren’t saved.

The restored contacts and contact groups appear on all your devices set up for iCloud Contacts.

If you change your mind, you can restore the contacts you were using. Just follow the steps above to restore the most recent version available.

Watch the GIF too

https://support.apple.com/kb/ph22730?locale=en_US

You cannot access iCloud on a browser on the iPhone. You have to use a computer. Log in on a computer using your browser and you can access iCloud. However, your contacts can only be restored there if you were using iCloud to manage your contacts.

You may get better and prompt responses if you may kindly provide the iPhone Model that you have and the iOS version if it is known to you.