This is a common issue, what if a issue shouldn't have root but you want to use that user to make a full backup of a system? They of course need root access.
You can actually just give them passwordless sudo access to rsync in /etc/sudoers:
sudo vi /etc/sudoers
yourusername ALL = NOPASSWD: /usr/bin/rsync
Here is how you would execute rsync:
The key thing for the remote host is to........