RC Filter vs Bypass Capacitor to Ground
I am confused with how to implement a method of filtering out the
impedance from the ground path of an IC

Ground path impedance is a problem that is conventionally solved by using a ground plane on a circuit board. This minimizes the impedance between grounds as much as is feasibly possible on a PCB. This works up to several GHz beyond which other problems can occur but given that most applications are below 1 GHz, a ground plane is the turn to solution.

I'm thinking that I should use an RC filter circuit in order to smooth
out the current and lower noise

No, that sounds like a disaster because it would put resistance in series with the ground feed and any current noise would become a problematic voltage noise.
Adding decoupling capacitor on all chips to a ground plane is also very sensible.