There is no way that a ground rod will create an RF Ground for your station. The earth is not a 'sink' for RF energy. The ground for your station is for AC safety and lightning protection only.
Your station ground rod must be connected to the AC mains entry ground rod by a #6 or larger wire - that is for the safety of you and your household as well as being a NEC requirement. The only exception is if the ground rods are 100 feet or more apart.

For curing "RF in the shack", look to your antenna system and use means to keep the RF off the antenna feedlines. Balanced antennas help, and running your feedline at right angles to the antenna for at least 1/4 wavelength will help a lot, and any antenna should have an effective common mode choke (some baluns qualify, others are poor) at the antenna feedpoint will keep common mode RF off the feedline.

Even at QRP levels, RF-in-the-shack can cause "strange happenings". A ground rod will not cure that problem.

Consider an 8 foot connection to a ground rod - at 28MHz the end of that grounding point will have a high impedance to 28 MHz RF - for an RF Ground, a very low impedance is needed, so any length of wire to the ground will not be effective for RF - in fact, it will do quite the opposite.

Bottom line - do not rely on a ground rod for an RF ground - it just will not be.

73,
Don W3FPR

Sun Jan 29, 2017 8:10 pm (PST) . Posted by:
"Tim McDonough N9PUZ" tim_n9puz
Most books and articles you read on creating a good RF ground for your
station rely on you having a very short run of cable from the common
ground at your operating location to the ground rod that's just outside
the basement wall or ground floor window of your shack. This is good
advice but my ham shack locations never seem to occupy a space near this
ideal ground rod. They are in an upstairs bedroom or the most difficult
corner of the basement possible.

The following article by Tim Ellison at Flex Radio Systems discusses all
of those "easy" situations plus offers some solutions for when that
ground point is a story or so above ground or 30 feet or more from your
only accessible ground point.

<https://helpdesk.flexradio.com/hc/en-us/articles/204779159-Grounding-Systems-in-the-Ham-Shack-Paradigms-Facts-and-Fallacies>

Tim N9PUZ