What you are looking for is a “MU-Plugin”– “Must-Use Plugin”.. Originally these were called “Multi-User Plugins” and were intended for exactly your purpose– to provide a way for site admins to enable functionality on all sites of an installation.
Create a directory at /wp-content/mu-plugins/ and put your PHP file(s) in it. WordPress will load the files automatically. MU-PLugins are “are automatically enabled on all sites in the installation” and cannot be deactivated except by physically removing the file.
Be sure to read the “Caveats” part of the Codex page.