A circle can have an infinite number of radii.
This is because a radius is defined as any line segment extending from the center of the circle to any point on its circumference. Since a circle's circumference consists of an infinite number of points, an infinite number of such line segments (radii) can be drawn. Imagine drawing a radius to every single point that exists on the edge of the circle; there's no limit to how many you could draw!
Therefore, the answer is infinite.