Create a shape layer. Expand the contents under layer. Delete current shape (i.e.: Ellipse).
Now create a path by clicking Right Arrow Icon (Next to Contents – Add) and add Path.

Now expand path and alt-click stop watch icon to add an expression.

Delete the current expression and copy-paste the following expression.
JavaScript
// Expression for a shape layer's Path property to create a spiral
// Slider Controls (add these to your layer):
// "Points" - Total number of points in the spiral
// "Start Radius" - Radius at the spiral's starting point (in pixels)
// "End Radius" - Radius at the spiral's ending point (in pixels)
// "Revolutions" - Number of full revolutions in the spiral
// "Rotation" - Rotation offset (in degrees)
var points = effect("Points")("Slider"); // Total points for the spiral
var startRadius = effect("Start Radius")("Slider"); // Starting radius in pixels
var endRadius = effect("End Radius")("Slider"); // Ending radius in pixels
var revolutions = effect("Revolutions")("Slider"); // Number of full revolutions
var rotation = effect("Rotation")("Slider"); // Rotation offset in degrees
// Enforce a minimum number of points to define a spiral
points = Math.max(points, 2);
var vertices = [];
var inTangents = [];
var outTangents = [];
var totalAngle = Math.PI * 2 * revolutions; // Total angular distance
for (var i = 0; i < points; i++) {
// Fractional progress from 0 to 1 along the spiral
var t = i / (points - 1);
// Interpolate radius between start and end
var r = startRadius + t * (endRadius - startRadius);
// Calculate angle for each point; add rotation offset
var theta = t * totalAngle + degreesToRadians(rotation);
var x = r * Math.cos(theta);
var y = r * Math.sin(theta);
vertices.push([x, y]);
inTangents.push([0, 0]);
outTangents.push([0, 0]);
}
// Create an open path for the spiral
createPath(vertices, inTangents, outTangents, false);
Now we need to add expression controls.

You need to manually connect the rotation slider to the Rotation parameter under Transform:

As shown from the image above you can simply click on the spiral icon and drag-connect it to any expression control. (First you need to alt-click stop-watch icon to create expression)

We can add a Trim Path as well to animate.

Here is the final result:
