Yes, you can set rules at the Organization level. The rules further allow you to select which Repos to apply them to and what branches on each repo.

This feature may be restricted to certain repo and subscription types:

Rulesets are available in public repositories with GitHub Free and GitHub Free for organizations, and in public and private repositories with GitHub Pro, GitHub Team, and GitHub Enterprise Cloud. For more information, see "GitHub’s plans." -- GitHub Docs - About rulesets