Yes, it is quite possible to integrate your Wordpress site to your Moodle site.

You can achieve this by using our plugin Edwiser Bridge.

This is how it works -

When you install 'Edwiser Bridge' on your WordPress site, then test connection and synchronize it with your Moodle site, all the courses on the Moodle site are synced to the Wordpress site, where a 'courses' page is created and then a user can buy a course from there. After purchasing the course, the user will be redirected to My courses page and then as they click on the enrolled course they will be redirected to Moodle for login.

When a new user comes to the WordPress site to purchase a course, he will have to register to the WordPress site again from the 'user-accounts' page provided by Edwiser bridge plugin. After registration, a new credential is created for the user and he can use those credentials to log in to the WordPress site and Moodle site too.

However, if a user has Moodle ID already, his login password will be different for the Wordpress site and the Moodle site and the user will have to change the password from the 'User-account' page so that the password for the Moodle site and Wordpress site becomes the same.