One way you can do this, is by drawing a circle on a canvas. You then use a custom dashed effect with the circle's stroke. Then, you animate the values of this dash effect, so that the circle's outline appears to grow around the circumference.
It looks like you can use the DashPathEffect to create the stroke patterns you need. Here is a StackOverflow answer showing how to use this.
You could then use an ObjectAnimator to animate the change in dash pattern.
--- EDIT ---
I just found a more complete answer on StackOverflow that describes in more detail how to use these two classes to animate a path.