Consider a general circle packing $\mathcal{P}$ in the complex plane invariant under a Kleinian group $\Gamma$ with finitely many $\Gamma$ orbits. Following the strategy developed by Oh-Shah, we prove an effective equidistribution for small circles in $\mathcal{P}$ intersecting any bounded connected regular set. In particular, in view of the recent result of McMullen-Mohammadi-Oh, our effective circle counting theorem applies to the circles contained in the limit set of a convex-cocompact but non-cocompact Kleinian group whose limit set contains at least one circle. We also consider the circle packing of the ideal triangle attained by filling in largest inner circles. We give an effective estimate to the number of disks whose hyperbolic areas are greater than t as t tends to zero, effectivizing the work of Oh.