Tribal Wildlife Corridors Act of 2021 This bill authorizes tribal wildlife corridors. Specifically, the bill permits an Indian tribe to nominate a corridor within the land of such tribe as a tribal wildlife corridor. The Department of the Interior must establish criteria for determining whether such a corridor qualifies as a tribal wildlife corridor, including criteria for restoring historical habitat. Interior must provide tribes with technical assistance to establish, manage, or expand a tribal wildlife corridor. Such assistance must include support with accessing wildlife data and working with voluntary private landowners to access programs for facilitating connectivity on nonfederal land. Additionally, Interior must (1) establish a program to award grants to tribes to increase connectivity through tribal wildlife corridors, and (2) consult with tribes to determine whether a tribal wildlife corridor may be expanded into public lands or otherwise benefit connectivity between public lands and such corridor.