Is there any instrument similar to a compass but which I can electrically drive? I would like to build a home weather station with analog instruments showing for example temperature, wind speed and wind direction.

I would like to use a salvaged flight instrument to show the wind direction: I have a wind vane transducer that convert the wind direction in an electrical signal and I would like to use this signal to drive a suitable instrument.

The instrument I have in mind is like a magnetic compass but while the magnetic compass does not need an "input signal" I need to drive the needle.

I have a look at a heading indicator 



but it seems to me that the "airplane needle" is fixed while the 0-360 graduation is moving. I need, like in a compass, a fixed graduation and a moving needle.

For example this seems fine to me but I have no idea what instrument is:

MASCO SERV. CORP.
DALLAS, TEXAS
PART NO. 503A
SER NO. 2500
Your best bet is to try and use an ADF readout, also known as a Fixed Card ADF (its most likely what you have pictured in your question). There are a few variants of the display out there and it will require some hacking to make it do what you need but it should suffice. As these units are generally considered "older" technology you may be able to get a read out for fairly cheap. On the even older side you can look for a Radio Compass/Radio Direction Finder which is quite similar. 

Note: A heading indicator is NOT what you want. While you could pull one apart and install some kind of drive system to make it do what you want it is not, as it stands what you want.