You could use Guzzle, there are some examples http://guzzle.readthedocs.org/en/latest/
Code depends on if you need to post or get to the api.
Take a look in vendor\laravel\framework\src\Illuminate\Mail\Transport, both MailgunTransport and MandrillTransport use Guzzle to access the service api's.
Solution
Thanks TerrePorter
For those who didn't have the clue like me to expose this Guzzle library to controller.
You can do on top of the controller
use GuzzleHttp\Client;
and then create Client's object as instructed in the Guzzle documentation
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