You need to make sure the required module “mod_rewrite” is enabled/loaded.
On Debian-based systems, one would run “sudo a2enmod rewrite” which creates a symlink “/etc/apache2/mods-enabled/rewrite.load” pointing to “…/mods-available/rewrite.load”
Not sure if CentOS has a similar abstraction or if you just have to create such a link yourself (or even manually issue the corresponding “LoadModule …” directive in some config file).