Open up your wp-config.php file, and search for
define('DISALLOW_FILE_EDIT', true);
Change true to false:
define('DISALLOW_FILE_EDIT', false);
For those who are using Siteground hosting define(‘DISALLOW_FILE_EDIT’, false); won’t work. Sitegound hosting provide SG Security plugin by default on direct WordPress installation from cPanel and it blocks the Theme Editor and Plugin Editor option by default.
To enable the Theme Editor and Plugin Editor option you just need to disable the option called Disable Themes & Plugins Editor under Site Security. Here is the path to disable that option :
Click on SG Security -> Site Security -> Disable Themes & Plugins Editor Option