See https://docs.docker.com/v1.6/installation/fedora/
“The docker command line tool contacts the docker daemon process via a socket file /var/run/docker.sock owned by root:root. Though it’s recommended to use sudo for docker commands, if users wish to avoid it, an administrator can create a docker group, have it own /var/run/docker.sock, and add users to this group.”
sudo groupadd docker sudo chown root:docker /var/run/docker.sock sudo usermod -a -G docker $USERNAME
Don’t forget to relogin to make this change take effect.