How to give a rise time to a square wave signal?

I am trying to simulate a circuit where the resistance of a potentiometer varies between two values according to the current flowing in the circuit. While I am getting a step resistance according to the input, I would like to have the change of resistance be a bit more gradual, and with a slope (linear or preferably an exponential growth and decay).

Above figure is my circuit. Below is my current output(left) and what I require(right) Is it possible to introduce such a gradual change?

Also is this the best way to introduce a varying resistance to a circuit?