Finally I can start the proxy with command:
sudo su tinyproxy -s /bin/sh -c 'tinyproxy -d'
or as a daemon with:
sudo su tinyproxy -s /bin/sh -c tinyproxy
Edit: Finally I found the right way:
(Sorry for a begginer's question, but hopefuly may be useful to simeone like me...)
systemctl enable tinyproxy systemctl start tinyproxy