C

Step 1: Understand the types of acceleration involved in circular motion. A particle moving in a circular path experiences two types of motion:
1. **Tangential Motion**: Acceleration that is directed along the tangent to the circular path; it affects the speed of the particle.
2. **Centripetal Motion**: Acceleration that acts towards the center of the circular path; it is responsible for keeping the particle in circular motion.

Step 2: For an object moving in a circle of radius $r$ at constant speed $v$, the centripetal acceleration ($a_c$) is given by the formula:
$$a_c = \frac{v^2}{r}$$
This acceleration is always directed towards the center of the circle.

Step 3: Since the question does not specify that the particle is accelerating tangentially (changing speed), we only consider the centripetal acceleration, which is directed along the radius of the circle.

Conclusion: The correct statement is that the acceleration of the particle is directed along the radius of the circle, hence the answer is Option C.