In your "make random pixels" loop, just exclude the pixel if it's outside your desired circle.
num_pixels = 20; // how many pixels
circle_radius = 32; // 32-pixel radius, or whatever you'd like
circle_radius2 = circle_radius * circle_radius;
while (num_pixels-- > 0)
{
// get a random number between (-circle_radius / 2, circle_radius / 2)
pixel_x = rand(circle_radius) - circle_radius / 2;
pixel_y = rand(circle_radius) - circle_radius / 2;
// compute squared distance between generated pixel and radius,
// exclude if out of range
if ( (center_x - pixel_x) * (center_x - pixel_x) +
(center_y - pixel_y) * (center_y - pixel_y) > circle_radius2 )
continue; // generate another pixel
// do stuff with pixel
}