What you are searching is a Rol that has the capability edit_themes which gives you access to the Theme Editor
and to edit theme files.
If you see this table only Super Admin
(multisite) and Admin
(single site) have that capability, so you need to add that rol to your users, now giving the rol admin
will be dangerous, what you can is either create a new Rol and add the capability to the new Rol, or add the capability to an existing Rol.