A charged particle (charge q) is moving in a circle of radius R with uniform speed v. The associated magnetic moment $\mu$ is given by

The current in circular path due to movement in circle is given by 

$i=\frac{q}{T}=\frac{qv}{2\pi R}$

Hence the magnetic moment associated with the particle is 

$\mu =iA=\frac{qv}{2\pi R}\pi R^2$

$=\frac{qvR}{2}$