cpanel doesn’t have letsencrypt integration yet but there is a feature request at https://features.cpanel.net/topic/provide-support-for-lets-encrypt-automated-certificate-management-ssl so you can add your vote for it there.
however, you need ssh access to run the letsencrypt client - so you might need to run the client on a separate VPS server with ssh access and then install the ssl certificate on your cpanel server
if you’ve never ran your own VPS server via ssh and installed relevant software, you can use an auto installer software - tooting my own horn, I develop CentminMod.com LEMP stack auto installer - which auto installs on CentOS, Nginx 1.9 with HTTP/2 support, PHP-FPM, MariaDB 10.0.x MySQL and CSF Firewall etc. So once installed on a VPS, you can run Letsencrypt client’s webroot authentication plugin to obtain the SSL certificate Letsencrypt Webroot Authentication Tested on Beta invited/whitelisted domain
and use and copy over the obtained SSL certificate to your cpanel server