Reaper doesn't record video.
The only workaround that I can think of: record your audio in Reaper, while also recording video using a separate app. Then import the video into Reaper and align it to the audio.
If you can't record audio in the video file for the sake of aligning the video to the audio recording in Reaper (since maybe recording 2 audio sources in different apps won't work), record the video with no audio but use the
clapperboard approach. You can even do this by clapping your hands together at the start of the video, or anything else that provides enough visual information of the exact moment of the audio spike you create in the process (for aligning it with the "clap" sound you record in the audio track).