As described on the Composer website:
curl -sS https://getcomposer.org/installer | php
sudo mv composer.phar /usr/local/bin/composer
Manual Method
you can run easier way to globally install composer than the manual proscribed in the github readme.md. It's actually on the getcomposer.org website:
curl -s http://getcomposer.org/installer | php
sudo mv composer.phar /usr/local/bin/
And you can try this way also, create an alias:
alias composer='/usr/local/bin/composer.phar'
Composer