Yes, there are. Often they are constrained to 270 or 240 degrees but the movement is capable of 360 degree motion. Olin describes the 2-phase sin/cos current ratio you need to drive them, but the search term you will need to actually find such a movement (and the specialized driver chips) is air core movement. They are not typically very available in small quantities - the one shown below has a hairspring to return it to the zero stop but that can be removed.
The driver chips such as CS8190 typically don't support 360 degree motion so you would have to roll your own.
More acessible, but not "analog" is the use of small stepper motors. Steppers require some way to find the absolute position at start-up. In automotive gauges they may just be run up against an end stop at turn-on.
The type used in many automotive applications is the X27.168 by Switec. Since, unlike air core gauges, they fail often, they can easily be found as replacement parts for GM cars.
Note that the standard unit has internal stops that limit the motion to 315 degrees and provide a zero reference - both of those things would have to be addressed to get true 360 degree absolute positioning.