Update wordpress Core Remotely

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You have several options:

  1. You can install WP-CLI – http://wp-cli.org/
    This will allow you to updates from the command line of your server.

  2. Use revision control, Git, Mercurial, etc. That way you just pull in updates to your staging server or localhost and push updates to your sever.

  3. Using a build script.
    You can have a build script located locally or on your server than will update wordpress for you via the command line or even cron job.
    There is a list of build scripts here: http://wpgear.org/ under “Command line fu”.

  4. Write your own bash/ruby/whatever script

  5. Use a plugin, there are several that have this as a feature.