Numerical simulations predict that molecular cloud collisions are traced by the 158 micron far-infrared emission line of ionized carbon ([CII]) and low-J CO rotational lines. Observations so far concentrated on CO because of a lack of [CII] data, and possible examples of cloud-cloud collisions based on CO are announced in the literature. Here, we report on the detection of high-velocity [CII] emission at +15 km/s in the DR21 region in Cygnus X that stems from a cloud that impacts with the DR21 cloud at a rest velocity of -3 km/s. The data were taken in the context of the SOFIA legacy program FEEDBACK, and indicate a bridge of emission between these two clouds in spectra and position-velocity diagrams. This scenario differs from the one previously suggested, based on CO observations, that the DR21 cloud is in collision with a cloud at +9 km/s (the 'W75N cloud'). We advocate that the [CII] 158 micron line is the best tracer for cloud-cloud collisions and look for further detections of this phenomenon in other molecular cloud regions.