I want to know if it's possible to realize a circuit described by the equation
$$I = \sin(w V)$$
where \$I\$ is the current, \$V\$ the potential and \$w\$ a variable which characterizes the single circuit.
A bit like a SQUID, which has a (ideally) sinusoidal response.
If your function is monotonic you could use some simple nonlinear circuit arrangement.
If your allowable values of wV cause the current function to be multivalued you could use a voltage-driven LUT (like an arbitrary function generator) and current source, but of course the resulting current would be dependent on the voltage history and initial conditions.
If what you truly want is a resistor, consider using a motor with a lever arm. The motor position (which can be servo-controlled to be a number of clockwise turns equal to V *W/(2*pi) ) will then put the end of the lever arm at an excursion which can be linkage-connected so that it drives a variable resistor. The negative resistance cases will be a bit of a problem, but a current driven positive or negative is a relatively easy thing to arrange (the resistor can span +1 to -1 volts, and a voltage-controlled current source driven from it).
A related probem, building a sinusoidal voltage-controlled oscillator, requires only proportioning a frequency to the input voltage, not holding any absolute phase relationship.
A common way to implement this is to use a piecewise-linear approximation to a sine curve, built using multiple resistors and diodes. One such implementation is described here, regarding the HP3311A function generator.