Abell 1240 is a merging galaxy cluster hosting prominent, symmetric double radio relics. To characterize its merging state, we provide the first weak-lensing detection of the dark matter distribution in the Abell 1240 field with Subaru/Suprime-Cam observations. Combining our new MMT/Hectospec observations with the spectroscopic redshifts from the literature allows us to investigate the cluster galaxy distribution as a proxy of the dark matter distribution. Both weak-lensing mass reconstruction and galaxy distribution appear to be elongated in the same direction as the X-ray surface brightness and reveal that Abell 1240 consists of two subclusters separated by ~1 Mpc between the double relics. We find that Abell 1240 favors being head-on binary mergers of an approximate 2:1 mass ratio. With the radio relic priors, our weak-lensing results suggest that Abell 1240 may be observed in the returning phase of the merger after the first collision.