With the exception of the Lead Link of the largest circle, Lead Links are assigned just like any other role.
However, the assignment must be made from the Supercircle. This is because a Circle, from its Supercircle's point of view, is just another role.
In the below example, there are two circles, the GCC circle and a Marketing circle that is inside it. The below view is from the GCC circle page, where the Marketing Lead Link is assigned.
If you click the person icon with the plus sign, to the right of the role, the following window will pop up:
How do I assign someone to a role?