Tribal Connect Act of 2017 This bill amends the Communications Act of 1934 to expand the Schools and Libraries Universal Service Support (E-rate) program to include support for Indian tribal libraries that are eligible for support under the Library Services and Technology Act (LSTA), without regard to whether the libraries are eligible for assistance from state library administrative agencies under the LSTA. The E-rate program provides discounted telecommunications services to certain schools and libraries. The Federal Communications Commission must establish a pilot Tribal Anchor Institution Program to provide E-rate support to tribes for institutions that are not schools or libraries, such as community centers. E-rate support may be provided to institutions designated by tribes if: (1) the tribes do not have existing libraries that are eligible for E-rate support; (2) the institutions are exclusively owned by the tribes; and (3) the institutions intend to deliver publicly available Internet access to students, teachers, librarians, and community members for educational purposes.