I only use it to access remote computers but, theres a systemd service file in /usr/share/anydesk/files/systemd/anydesk.service
You can copy it to /etc/systemd/system and then enable the service
cp /usr/share/anydesk/files/systemd/anydesk.service /etc/systemd/system/
systemctl enable anydesk
systemctl start anydesk
That should probably work, let us know if it does.