Yes. Just in front of us you will see a Zoom audio recorder on top of the uke case. The one I am using is the Zoom H2n. It is very good and easy to use too. You just have to make sure that the recording level is correct and not distorting. The video was recorded on a simple compact camera.
I process the audio on Audacity, a simple free app for Mac and PC. I add a little compression, a touch of reverb and increase the dynamics to max. I export it as an MP3. Put the MP3 and the video file together on your favourite video program and you are finished.