Access to Care for Overseas Military Act This bill requires the Department of Defense (DOD) to establish a medical readiness program to (1) develop relationships with partner nations in the Indo-Pacific region, (2) facilitate the improvement of medical care during peacetime and wartime, and (3) maintain strategies and policies of DOD for medical readiness in the region. The Office of the Under Secretary of Defense for Personnel and Readiness must submit to Congress, not later than September 30, 2025, a strategy for the implementation of the program. DOD must establish the program by January 1, 2027.