Interstate Teaching Mobility Act This bill amends the Elementary and Secondary Education Act of 1965 to establish a voluntary interstate teaching application program for participating states. To participate in the program, a state must require sufficiently rigorous assessments in awarding a teaching license or certification. In carrying out the program, the Department of Education shall: create an electronic application process for eligible teachers who are licensed or certified in a participating state to apply for teaching positions in another participating state; require a participating state to recognize the teaching licensure or certification of each such teacher without the teacher having to complete additional licensure or certification requirements; ensure that a participating state maintains specified eligibility requirements; and provide technical assistance. A teacher seeking to participate in the program must submit an application containing: (1) proof of active licensure or certification in a participating state, and (2) the teacher's results on specified assessments.