Dome Fuji, on the Antarctic plateau, is expected to be one of the best sites for infra-red astronomy. In Antarctica, the coldest, driest air on Earth provides the deepest detection limit. Furthermore, the weak atmospheric turbulence above the boundary layer allows for high spatial resolution. We plan to perform site-testing at Dome Fuji during the austral summer of 2010-2011. This will be the first observation to use an optical/infra-red telescope at Dome Fuji. This paper introduces the Antarctic Infra-Red Telescope with a 40cm primary mirror (AIRT40) which will be used in this campaign; it is an infra-red Cassegrain telescope with a fork equatorial mount. AIRT40 will be used for not only site testing (measurement of seeing and sky background) and daytime astronomical observation during this summer campaign, but also for remote scientific observations during the 2012-2014 winter-over campaign. For this purpose, AIRT40 has to work well even at -80 degree Celsius. Therefore, we accounted for the thermal contraction of the materials while designing it, and made it with special parts which were tested in a freezer. For easy operation, many handles for transportation and a polar alignment stage were installed. Moreover, we confirmed that this telescope has enough pointing, tracking, and optical accuracy for the summer campaign through the test observations at Sendai, Japan. Because of these preparations AIRT40 is suited for observations at Dome Fuji. In the 2010-2011 campaign AIRT40 will be used to measure the seeing, infra-red sky background, and to observe Venus.