Certificate-based authentication is not part of HTTP, but is part of the SSL / TLS protocol.
cURL :
$ch = curl_init('https://example.com/');
curl_setopt($ch, CURLOPT_SSL_VERIFYHOST, '1');
curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, '1');
curl_setopt($ch, CURLOPT_CAINFO, '/path/to/cert/ca.crt');
curl_setopt($ch, CURLOPT_SSLCERT, '/path/to/cert/client-cert.pem');
$response = curl_exec();
curl_close($ch);
. curl_setopt.