Collegiate Housing and Infrastructure Act of 2020 This bill allows tax-exempt charitable or educational organizations to make collegiate housing and infrastructure grants to certain tax-exempt social clubs (e.g., college fraternities and sororities) that apply such grants to their collegiate housing property. A collegiate housing and infrastructure grant is a grant to provide, improve, operate, or maintain collegiate housing property that may involve more than incidental social, recreational, or private purposes. The grant must be for purposes that would be permissible for a dormitory or other residential facility of the college or university with which the collegiate housing property is associated. The grant may not be used to provide physical fitness facilities.