Is there a gem or a technology that can make live video streaming via webcam with rails?
RoR (or anything similar really) isn't relevant here. Fire up Flash Media Server or Red5 and utilize a Flash player.
First you need to encode the video with something. Flash Media Live Encoder will do the trick. This will take audio/video inputs and compress it down, usually to H.264 or VP6. It then sends the stream data to your server.
Your server (such as Red5) takes this data and distributes it to clients.
On the client side, you need something to play this video. Flash is still the most compatible (currently anyway... HTML5 will change that). A common Flash video player is JW Player, but you have other choices as well.