Yes, some aircraft do have them. For the 2 aircraft types that I've operated which had such a system, a vibrating probe was placed in an ice-sensitive area, and, when iced up, the lower frequency of vibration trigerred an icing alert. This type of system is periodically de-iced by heating, allowing for on-going detection of further ice build-up.
On one type which I flew it was very good, as confirmed by the 'traditional' ice detection procedures. The B777 detection system has an Auto function to activate Nacelle heat etc., but several operators have encountered icing problems undetected by the system, and the Automatic system is utilised as a back-up to more traditional pilot detection and prevention procedures.
There are other types, other posters will no doubt advise.