The magnetic moment of a current loop can be defined as the product of the current flowing in the loop and the area of the circular loop, $M=IA$

When a wire is bent to form a circular loop then its area is $A=\mathrm{\pi }{\left(\frac{L}{2\mathrm{\pi }}\right)}^2$

Therefore, magnitude of its magnetic moment is $M=\frac{L^{2}I}{4\mathrm{\pi }}$