http://rafalgicgier.com/gf-front-end-login-register/

gf.php

<?php
// the _3 prefix has to match the id of the form you have created
add_action( "gform_after_submission_3", "login_form_after_submission", 10, 2 );

function login_form_after_submission($entry, $form) {

	// get the username and pass
	$username = $entry[1];
	$pass = $entry[2];

	$creds = array();

	// create the credentials array
	$creds['user_login'] = $username;
	$creds['user_password'] = $pass;

	// sign in the user and set him as the logged in user
	$sign = wp_signon( $creds );
	wp_set_current_user( $sign->ID );
}